Compressed air and thermal aren’t economically viable, which is why decades after introduction there isn’t large scale deployments of the stuff.
> Any sort of heat utilization or recapture massively increases efficiency for some of those ideas.
Low grade heat has minimal to zero economic value. This is why nuclear power plants need to build cooling towers etc rather than having something useful to do with all that heat energy. There’s some very niche utility, but it’s competing with other extremely cheap sources of heat like solar thermal which itself has barely catch on despite rapid payback periods.
There was no need for compressed air or thermal energy storage until recently. In fact, there were no large scale battery energy storage systems until recently either. All of them are starting to happen.
Your point about low grade heat is entirely a red herring. It’s not even true as storage of low grade heat is valuable in a renewable energy world. But more importantly those energy storage can definitely store higher grades of heat. Especially if it is hot enough to drive a turbine, or used to that heat to make other systems more efficient. In large scale facilities, it is not meaningfully less efficient that batteries. So the conclusion is the same: there does not really need to be batteries for this purpose. You can eliminate them and save yourself the money. After all, you already admitted that you need those other systems anyways, so just have those other systems and not bother with batteries.
And you're consistently ignoring the part about not everything needing electricity exclusively. Any sort of heat utilization or recapture massively increases efficiency for some of those ideas.