There are no good universal generalisations relating bond-type and bond strength in crystals
The problem with answering this question is that the assumption you start with is just wrong. There are no good universal rules relating bond-type and strength. I'm not sure why this generalisation is so common (there are a number of similar questions scattered across this site and very few good answers) but I blame naive teachers not wanting to face the issue of how complicated chemistry is.
Let me illustrate the problem with the generalisation with some examples. First, if ionic bonds are always stronger, how do you explain the existence of ionic liquids (used in some industrial processes to avoid organic solvents)? 1-butyl-3-methylimidazolium hexafluorophosphate, for example, consists of two bulky ions but the ionic attraction isn't even strong enough to hold together a crystal at room temperature. Graphite and diamond are covalent compounds that have high melting points. But diamond forms strong crystals and graphite is soft enough to be a lubricant. Sodium chloride is an ionic compound and (table salt) forms moderately strong crystals but has a high melting point. Iodine is a covalent compound but its crystals are so weakly held together than it has a notable vapour pressure at room temperature and will rapidly evaporate on modest heating.
What explains these disparate observations is not the type of bonding but the structure of the compounds. The archetypal "weak" covalent compounds (possibly the source of one bad generalisation in teaching) do not consist of crystals held together by covalent bonds at all. Iodine crystals consist of I2 molecules (with covalent bonds between iodine atoms) but the crystals are held together by (much weaker) van der Waals interactions, hence why they evaporate so easily. NaCl consists of a crystal lattice where all the bonds are ionic. It is relatively strong and the bonding explains its properties. Ionic liquids also have ionic bonds but the ions involved are large and "floppy" which means the strength of the ionic attraction is far lower than in NaCl which explains why they are liquids.
Diamond and graphite form a particularly interesting pair (both consisting only of carbon). Diamond is a massive network where every carbon is connected to every other carbon in a near-infinite tetrahedral array. It is extremely hard and doesn't melt easily. The structure of graphite has two types of bond holding its structure together. It consists of flat planes of hexagons of carbon (like a lot of benzenes fused together) held together by covalent bonds (some delocalised across the whole plane). These bonds are strong but the planes are held together by van Der Waals forces between the planes which are unusually strong because they cumulate over the whole large plane. But they are much weaker and less rigidly directional than the covalent bonds in the plane. As a result the planes can slip against each other making graphite "soft" enough to be a useful lubricant (though it is also worth noting that this softness is non-isotropic and the individual planes are strong in two dimensions which explains the extraordinary tensile strength of graphene which is, effectively, an isolate plane of graphite).
The point of these examples is to illustrate than any generalisation about the type of bond and the strength of a crystal is meaningless in general and only makes sense of you understand the structure involved.
The false generalization that ionic bonds are stronger probably arises because many simple compounds taught in schools seem to follow it. But the examples (iodine versus NaCl, for example) conflate the bonding in the bulk crystal with the bonding in the molecules in the crystal. Iodine might better be described as a van der Waals crystal: the molecules have covalent bonding but the crystal does not, being held together by much weaker interactions.
Ionic liquids have ionic bonding, but this is weak because the ions are large, vastly lowering the strength of the ionic interactions.
Some covalent solids do have covalent bonds across the whole crystal (or large parts of it). They do tend to be strong, sometimes. But, as the examples of diamond and graphite illustrate, you still need to understand the structure to explain all the properties. Individual planes of graphite are "strong" but the planes only stick together with weak forces.
All this makes the generalisation that "ionic bonds are stronger than covalent bonds" pretty useless. But, if you understand the structure of the specific crystals you can usually explain the strength.