It seems to me that most of the responses here are not really getting at the heart of the issue. Saying that the term "aqua" is used instead of "water" because of regulatory reasons is merely pushing the question back one step, leaving us still to wonder why the people who created those regulatory rules decided that the term "aqua" should be used to indicate the common substance water (H2O) on cosmetic product ingredient lists. User bot47 alluded to this in his/her question above.
What was the primary reason for regulations requiring the use of "aqua" to mean water on cosmetic ingredient lists? I don't think that the primary motivating factor behind that regulatory rule was clarity or understanding across different regions/languages, because the Latin word "aqua" is not a word commonly used for "water" in any living language that I know of -- certainly not in any of the world's most common languages, such as English, Chinese, Spanish, Arabic, etc.
In English, the term "aqua" only means "water" in a technical usage (like on cosmetic labels), and otherwise "aqua" refers to a blue-green color (like "aquamarine") or is found in water-related words like "aquatic" or "aquarium." I think that if you asked a person on the street, "What is aqua?" without any other context, they would mostly likely be confused about your meaning. They might guess that you are referring to something water-related, or they might have no idea what you mean.
Some people might think of Latin as a universal language of science, and therefore universally understood, but most people do not speak Latin no matter which part of the world you are in. The language spoken by the most people in the world, Mandarin Chinese, bears no meaningful relation to Latin. While Spanish "agua" sounds similar to "aqua," one cannot require the consumer to assume that a similarity in spelling/sound reliably indicates an equivalent meaning. If "sugar" were labeled using its Latin translation "saccharum," then consumers might mistakenly assume that the product contained the artificial sweetener saccharin instead of actual sugar.
If clarity were the main reason for the regulation, using English "water" or the chemical formula "H2O" would, I suspect, be better understood than "aqua." No one language is going to be perfectly understood in every situation, but English is arguably the single most widely understood language in the world, and "water," being a common word, is reasonably likely to be understood even by someone with only a scant knowledge of English. This is why many terms on the INCI list are in English or use the scientific name for a plant species (in Latin per scientific convention) followed by English terms providing further information. Examples: The INCI term for "beeswax" is "Beeswax," for "raspberry extract" is "Rubus Idaeus (Raspberry) Fruit Extract," and for "sunflower oil" is " Helianthus Annuus (Sunflower) Seed Oil." The only reason Latin is used in the names of these substances is that this is the standard way to refer to a specific species of plant unambiguously. For instance, Rubus ideaus refers to the species also called "red raspberry" or "European red raspberry," which is different from Rubus strigosus (American red raspberry), Rubus crataegifolius (Asian raspberry), Rubus occidentalis (black raspberry), Rubus ellipticus (yellow Himalayan raspberry), or many other raspberry species. In order to accurately and precisely label the plant species used in an ingredient, such that there is no ambiguity, it is most practical to use the scientific name for the plant, which is in Latin by convention. (Thank you, Carl Linnaeus.) If we extend the same spirit of employing the specific, unambiguous labels used in scientific writing to the topic of interest here, we should be using the term that is typically used in science to refer to water, and that term is "water." I have studied and worked in science for years, and I gave only ever heard of water referred to as "water," "H2O," or (humorously) "dihydrogen monoxide" (the last one being a tongue-in-cheek joke about chemistry nomenclature).
I suspect, as the the OP and some early commenters suggested, that the primary reason that "aqua" is used instead of "water" is that people don't like the idea of paying for water in their products, even if the inclusion of water is necessary and justified for scientific reasons. Perhaps this is a surprise for some people, but human beings are irrational creatures, by and large.
Let me digress to emphasize this point a bit: In my home country, the USA, not only are people irrational, but they tend to have a very poor understanding of science. As one example of this, a 2015 survey found that 82% of respondents supported mandatory labels on foods "produced with genetic engineering," which refers to GMO's (genetically modified organisms). In the USA, at least, "GMO" has become a dirty word, and food labels commonly boast their their products are "GMO-free" in order to appeal to consumers. However, in that same survey where 82% wanted mandatory labels on GMO foods, presumably because these people thought GMOs were harmful, 80% (nearly the same number of people) also supported "mandatory labels on foods containing DNA." These people apparently did not understand that DNA is a normal part of all living organisms on earth, and that we eat these organisms (or parts of them) for food. All food item containing plant or animal cells or single-celled organisms would require this ridiculous label warning about "DNA" that 80% of Americans favored -- this label would include everything from apples, oranges, potatoes, broccoli, and carrots, to fish, steak, milk, cheese, and eggs, to wheat, oats, rice, nuts, and soy, and anything made using such ingredients). The only DNA-free items would be highly refined and purified substances such as table salt, table sugar, cooking oil, or water.
My point in bringing up this survey is that the vast majority of Americans know very little about science, and so they are likely not to read any ingredient list with a particularly informed or critical eye, and they are prone to illogical conclusions about what they see. As a result, no matter what the explanation is for why water is the first ingredient on the list of ingredients in a fancy/high-end/expensive product, pretty much nobody will be pleased or impressed by the fact that water is the single largest component of this thing which is supposed to make them feel special, refined, exclusive, etc.
First of all, for the typical consumer who is buying cosmetics, water is cheap, so the consumer might feel like they were cheated in a way, being charged top dollar for something that comes out of their faucet at home. And secondly, this fancy product that they're purchasing is supposed to be special and improve their appearance or fix a cosmetic problem -- in some ways, many consumers will expect it to contain only the rarest, most exotic ingredients that will be different than what they've used before -- and so people will tend to wonder how "water," which they already use on their skin every day, could possibly provide an additional benefit for them. "Water" in a list of ingredients probably comes across to many people as an inert filler which may, if anything, be impeding the action of the other, more important ingredients.
(I realize this line of thinking is not entirely logical, but I think the vast majority of people would tend to have this reaction on some level. It's well-established that irrational thinking influences people's decision making all the time and in many ways.)
At best, people might feel neutral about seeing "water" on a label, recognizing that there are legitimate reasons for water's use in a formulation, even in luxury products with other rare/expensive ingredients. But on average, the disclosure of the aqueous nature of a product, especially those aiming to be seen as high-end or luxury items, will decrease the product's appeal among consumers. In the same way, no matter how delicious a $100 bowl of soup from the world's best chef tastes, nobody will feel even better about it after being reminded that the main ingredient in that dish was water.
Using "aqua" obscures the fact that water is used in a product, which will be favorable for most products' sales, which is really what cosmetics companies care about. "Aqua" may even sound like something good to some consumers, giving the product some mysterious appeal ("Oooh! 'Aqua'... I wonder what that is! Must be fancy...") If anyone asks a cosmetic company about this term, then various explanations can be rolled out: the notions that "aqua" is universal, that it is less English-centric and therefore more culturally sensitive across many markets, or that it's a scientific term and therefore inherently preferable to use. However, all of these explanations are disingenuous and avoid what is likely the real reason (improving the company's bottom line), but are they just plausible enough to allay suspicion and discourage follow-up questions.