Why would anyone run an energy storage system for general population in that system? If they can undercut the energy companies at some times and sell to the Bitcoin miners, why would they even bother with residential customers?

Sure, people who can afford energy storage themselves would be sorted. (Most of the time) Anyone below that wealth threshold would be at the mercy of "am I more important than the monetary gain today".

It could be profitable. But miners will buy energy as long as the price is lower than the expected return, regardless if it comes from excess renewable or from storage, do it may be more profitable not to. This means a bidding market between the miners and tenants for the stored energy. And that's not the uncertainty I want to live with every day. (Because that market is no longer realistically possible to regulate given the energy producers become the bank, the mint, and the business running them)