Tegmark cosmology implies not only that there is a universe which runs this one as a simulation, but that there are infinitely many such simulations.

I'm not sure that this is true. My understanding is that IF a universe which runs this one as a simulation is possible, THEN Tegmark cosmology implies that such a universe exists. But I'm not sure that such a universe is possible. After all, a universe which contains a perfect simulation of this one would need to be larger (in duration and/or size) than this one. But there is a largest possible finite simple group, so why not a largest possible universe? I am not confident enough of my understanding of the constraints applicable to universes to be confident that we are not already in the biggest one possible.

There is a spooky similarity between the Tegmark-inspired argument that we may live in a simulation and the Godel/St. Anselm-inspired argument that we were created by a Deity. Both draw their plausibility by jumping from the assertion that something (rather poorly characterized) is conceivable to the claim that that thing is possible. That strikes me as too big of a jump.