The SA doesn't add an iota of complexity to our model of reality - ie physics. It's a predicted consequence of running physics forward.

Not necessarily. Given our understanding of the laws of physics, simulating our universe inside itself would be tough. Note that nothing in the simulation hypothesis requires that we are being simulated in a universe that has much resemblance to our apparent universe. (Digression: Even small amounts of monkeying with the constants of the universe can make universes that can plausibly give rise to life. See here (unfortunately everything beyond the summary is behind a paywall). And in some of those cases, it seems plausible that large scale computation might be easier. If certain inflationary models are correct then there should be lots of different universal bubbles with slightly different physical laws. Some of those could be quite hospitable to large-scale computation.)