I suspect this may be 80% of the problem with leads in Minecraft, and I believe this mod may be the right place to address it:

When a leashed mob is pulled towards a 1 block high step, the game waits for the creature to perform a jump to get up the ledge. This action essentially guarantees the creature will fall behind and break its lead, as it is a delayed function and highly subject to server performance (as well as just plain unreliable).

So, my suggestion here is to add a (random) patch to allow all land-based creatures to step-up a block just like horses do, while leashed.
I hope this can be considered, as it will be a major step towards making leads a viable tool. Thank you.