Finding a suitable English translation of "An old donkey pulls all the weight all alone"

These aren't idioms I've heard, but how about:

"The older the horse, the heavier the burden"

Or to reverse the idiom of "The chain is only as strong as the weakest link", you could say:

"The strongest link in the chain has to hold the others together"

If I haven't answered it correctly, I at least hope I've gotten close.

A related saying might be, "If you want something done right, you have to do it yourself." It definitely has the connotation of not being able to rely on other people (particularly subordinates) to do something. But it doesn't really imply that therefore all the work falls on you.

"It's lonely at the top", possibly?

A vaguely comparable English catch-phrase is, "If you want to get something done, give it to the person who's busiest." The idea being, people who are competent and industrious tend to take on all the work, and people who are sitting around doing nothing are often in that position because they are either too lazy to do the work that's given them or because they are so unreliable that no one trusts them with any important work.