[throwawaymath]

That's technically correct (the best kind of correct!), but I think it's a misleading thing to state. The reason all objects eventually become spherical is because they eventually disintegrate into the nearest significant source of gravity, which will itself be a sphere. It's not as if, hypothetically speaking, an immortal human being floating through space without orbit would eventually morph into a sphere under the pressure of its own gravity. Rather any object is naturally going to decompose into parts which will be spherical or adjoined with an already spherical object.

Even if the conjecture that sufficiently high entropy causes quantum physical effects to dominate macro-physical spacetime is correct, long before that happens there won't be any objects left which aren't already spherical.