Basically, everything about it is hard. Very high pressure and low temperature, leakage, steel walls get brittle, etc. It's a nightmare, doable, but very hard to scale.

The most promising solutions I've seen are taking advantage of the fact that single H+ “dissolves” into metal under pressure. You store that saturated metal and heat it when you want to release it. That way energy density starts to make sense. This video shows one such approach:

https://www.youtube.com/watch?v=M0fnEsz4Ks0

Binding it with carbon seems promising as well, but I wouldn't bet on simply trying to jam it as a gas in a tank.

But I'm not an expert, just very interested on the subject for many decades.