Yes, and that's the problem. What Zhang et al [2] showed convincingly in the Rethinking paper is that just focusing on the hypothesis space cannot be enough since the same hypothesis space fits real and random data so it's already too large. Therefore, these methods that focus on the hypothesis space have to talk about a bias in practice towards a better subspace, and that already requires studying the specific optimization algorithm in order to understand why it picks certain hypothesis over others in the space.
But once you are ready to do that then algorithmic stability is enough. You don't then need to think about Bayesian ensembles, or other proxies/simplifications etc. but can focus on just the specific learning setup you have. BTW algorithmic stability is not a new idea. An early version showed up within a few years of VC theory in the 80s in order to understand why nearest neighbors generalizes (it wasn't called algorithmic stability then though).
If you are interested in this, also recommend [3].
But once you are ready to do that then algorithmic stability is enough. You don't then need to think about Bayesian ensembles, or other proxies/simplifications etc. but can focus on just the specific learning setup you have. BTW algorithmic stability is not a new idea. An early version showed up within a few years of VC theory in the 80s in order to understand why nearest neighbors generalizes (it wasn't called algorithmic stability then though).
If you are interested in this, also recommend [3].
[2] https://arxiv.org/abs/1611.03530
[3] https://arxiv.org/abs/1902.04742