As stated in [1] they use a variant of "Simple and Efficient Construction of Static Single Assignment Form" [2], which does not require a dominator tree (or a liveness analysis).
[1] https://github.com/golang/go/blob/master/src/cmd/compile/int...
[2] http://pp.info.uni-karlsruhe.de/uploads/publikationen/braun1...
You don't need to add every optimization known to man to a compiler, so you can sometimes keep a few of the important ones and then skip every other optimization. A priori, I'd guess SSA would speed up the compiler, which means you end up having a better budget for the more expensive optimizations.