Do researchers know/have theories as to why evolutionary lines seem to cap at three stages?

It’s an issue of power, anonymous. At the third stage, a pokémon is usually at its peak potential without any enhancements. Pokémon don’t really have the sort of energy to achieve an evolution beyond the third stage, as the power involved in such a state would be extremely difficult for a non-legendary to control and highly risky for a pokémon’s physical form to contain.

This is, incidentally, why mega evolution is a temporary process and why many pokémon experience berserker states when first tapping into it. The mega evolution stone is essentially a catalyst that unlocks any remaining potential a pokémon has and pours it into their forms all at once. As this potential is usually not enough to trigger a full-scale evolution by itself, the stone provides an additional boost of energy, which often far exceeds the amount a pokémon is capable of handling. The end result is not only that blind rage but also the inability to hold that form permanently. After a while, if forced to maintain their mega evolved state, a pokémon will revert to their original forms on their own, as their energy will simply be completely spent.

But the point is, the reason why pokémon can only evolve twice at most is because they just don’t have enough—power, energy, aura … any one of those, depending on which researcher you ask—to achieve proper evolution for a third time. The closest some will ever come is mega evolution, which is half external anyway.