Imagine that some Clarktech version of ourselves dedicates an entire galaxy to simulating the Milky Way. Would we have noticed by now?

Neither does the simulation need to be perfect: it only needs to be perfect wherever we actually look. This makes for a much more complex program, but might save on computing costs.

Anyway, yeah, you probably won't get an infinite chain, but you'll get a very long one, which leads to my second point:

A "singleton chance simulation" just means that someone randomly decided to simulate our universe in particular. This is rather unlikely.

A "dynamic equilibria of nested simulation" just means that Universe A simulates Universe B simulates Universe C which simulates Universe A, creating a descending chain that is not as dense as an immediate recursion, A->A->A.

Both these cases will contribute less possible universes than a (near-)infinite descending chain, so by eliminating the descending chain you've greatly decreased the probability of being in a simulation.