This is not a problem specifically related to MMOs; single-player games often have level caps as well, and the fundamental reason for introducing them is the same.
It's much easier and more practical to balance for a fixed range of progression than an infinite one.
You postulate that one could just implement a "mathematically designed leveling system that keeps the leveling experience interesting and endless" but this is much harder to do than it is to say (assuming you still want "fun"). Essentially all this is doing is finding power curve that isn't too shallow or too steep and using that curve to scale a player's statistics.
This is not likely to remain interesting for a long time. It lacks variety. It's just numbers getting increasingly bigger, and while that may entertain a few people for a little while you will eventually reach the point where the numbers are too big to be effectively comprehensible (42,132,927,189,100 strength) and don't have an appreciable impact (you might deal 92,101,626,001,292 damage per second at level 67,192 but enemies your level have a similarly inflated HP score, so it still takes you the same amount of time to actually kill them as a level 67 player).
Players are usually engaged by progression that introduces variety and choice (for example in the array of abilities they can chose from). A secondary effect in the introduction of choice is the ability to plan, to elect abilities or skills or gear that synergizes with itself in a particular way. While many games end up with some of those synergies organically, at least a good portion of them are initially planned for; it's much harder to ensure that sort of opportunity for fun exists in a system where abilities are randomly-generated and made available.
A system with procedurally-generated progression breakpoints is totally possible. It's hard to tune into something fun, though, because the more procedural variety you introduce the less designer control for fine-tuning you have. This means the designer is often forced to balance against the potential components of an ability set, not the abilities themselves. For a concrete example of such a thing in a small (non-infinite scale), consider the original Guild Wars and its expansion chapters. Each chapter introduced a large new set of skills, and player progression was mainly measured in skills and not level (which was capped at 20). Balancing for that combinatorial explosion was extremely difficult and allowed several undesirable, unbalanced (both over and under powered) combinations at times. That's why Guild Wars 2 chose to go with a much more directed and focused system.
A fully-procedural progression breakpoint system would be interesting, but nobody's tried/done it well yet -- and besides, assuming a perfect implementation of such a thing, you wouldn't necessarily need levels at all at that point.
There is a related discussion, and that is about capping lower than you eventually expect to allow (for example, how Diablo 3 initially capped you at 60, and GW2 at 80). This allows you to still design for a fixed range of progression but also expand that range somewhat -- offering new rewards and other such carrots -- to players who purchase expansions at a later day. WoW also does this, of course, but like the above it is not strictly anything to do with MMOs.