Saying that last bit about time is not particularly meaningful for two reasons.

First of all, we do not especially know the end state of the universe. It may not be true that all matter decays, and protons may be stable. We may be in a false vacuum which will spontaneously collapse in large timespans.

Second of all, the hypothetical is a thought experiment. The monkeys are a placeholder for any random generation of characters. The though experiment also does not take into consideration the food required to feed monkeys for infinite time, nor their aging, mutation over generations, and waste logistics. It's not meaningful then to suddenly decide to apply the laws of physics to them. The only laws applicable in this scenario are logic and mathematics.

I generally agree with the rest of your take, although I disagree where you say the thought experiment is dumb. I only have an issue with that last point lol. Cheers.