But if that limitation is repetitive to the point of investing in infrastructure to use EVs, then some other large-scale investor will close that arbitrage opportunity.

Basically, the next-day / week energy markets, where EV owners can compete, will be saturated by grid-scale battery operators. Renewables will leave large gaps for seasonal energy needs - for example two weeks of winter with no sun and no wind - but EVs cannot help there. So some spin on-demand non-renewables will need to cover that (i.e., the current main providers, after becoming too expensive to run due to carbon pricing).