I have read about "electroflocculation" that uses less flocculant/alum, but is there a method – no matter how expensive or impractical – that uses no flocculant at all?
This of course depends on the scale and intent of the purification/treatment process, but flocculation is but one step in the water treatment process. So, I'm not sure whether you are asking if you can purify water without flocculation, or if you can get flocculation/aggregation to occur without the addition of floccing agents.
The simplest answer to water purification, on a small scale, is filtration and distillation. Flocculation serves to remove solid particles from the water which contribute to turbidity, but which may also include pathogens that are of real concern to human safety. On larger scales (household to community), incredibly effective methods for removing these types of contaminants include various forms of filtration. Some of the first successful water treatment plants on a large scale used sand filtration, and fast and slow sand filters are still used widely today. There are many commercially available drinking water filters for the removal of sediment, microbes and chemicals which are highly effective. Of course, on an industrial scale, filters of this nature would require frequent changing, and this is where sediment removal via flocculation is most effective in reducing costs. You could Google 'water purification in developing worlds' for a range of water purification methods that do not involve flocculation.
On the other hand, inducing flocculation without the addition of flocculant again depends on nature of the contaminant you wish to remove. The biofuel industries are pursuing this goal, developing methods of harvesting valuable microalgae stocks. Autoflocculation (or bioflocculation) of microalgae is known to occur as a function of pH, which can be controlled by restricting CO2 levels. Again a Google search on 'microalgae autoflocculation' will give you many hits. Another method is the light induced autoflocculation of microalgae. There is an interesting post on ResearchGate that may be of some interest to you if you are focused on flocculation of microalgae (if not, then ignore!)
Sure. We could imagine, for instance, that a strong electrical field (anode/cathode pair) and a special stirring, would cause the migration of all non-H2O molecules to nucleate together and/or adhere to walls and be removed from solution.
Flocculants just start this process going, and are used in context to other processes, as @long mentions.