It's about cost per Kwh stored — hydrogen does indeed have better energy density, but if it costs 10 times more than CAES to store one megawatt hour of energy, no one will finance it. Do some money calculations with some basic assumptions for a utility, and you'll see why they are very hesitant to build anything that isn't a moneymaker immediately (CAES included!).

CAES is interesting because you can recycle some (keyword, SOME) existing mines for enormous energy stores, and the hardware needed to build CAES on said mine is not particularly special and easily understood for engineers, and therefore cheap, and also easy to handle safety-wise. Air that leaks makes only noise. Hydrogen that leaks tends to catch fire, and burn with a non-colored flame that is hard do see, and therefore a large safety challenge.

To compress hydrogen beyond the energy density of CAES or petroleum products, you still need comparatively expensive hardware. I think the price of these things will come down, as you pointed out, but I have a hard time seeing hydrogen electrolysis tech ever being grid scale. Maybe you'll have one attached to your house like the Tesla batteries, though, paired with solar panels.

> For those long storage times, there are proportionally fewer charge/discharge cycles, so the cost of the hydrogen itself becomes proportionally less important.

The key with large scale energy storage is to do price arbitrage — store energy when it is cheap (e.g. at night), sell it when energy is expensive. A utility won't sit on a large (say, 300 megawatt hours) hydrogen store for long, because once the cost to sell it exceeds the cost to store it, they are looking to put that energy back on the grid, even if it is for a specific use case like peak shaving. Grid scale projects need to be financed and paid off in 30-50 year timescales, usually. The main sources of cheap hydrogen (as in, cheaper than bulk liquid natural gas) are industrial processes that produce hydrogen as a byproduct.