You are using long-term in an extremely vague way.
Pumped hydro is not a solution for seasonal storage or yearly storage. Seasonal variation can be a problem in higher latitudes.
For example we have a serious problem in New Zealand where our existing "green" hydro lakes are sometimes low and our economy is affected: creating national power crises during dry years. We use coal-burning Huntley and peakers to somewhat cover occasional low hydro generation.
Unfortunately our existing generators also have regulatory capture, and they prevent generating competition (e.g. new solar farms) through rather dirty tactics (according to the insider I spoke with).
Apparently much of our hydro generation is equivalent to “run-of-river” which requires the river to flow. Although the lakes themselves are large, they don't have enough capacity to cover a dry year.
NZ had planned a pumped hydro, but it was expensive: planned cost of 16 billion compared against total NZ export income of ~100 billion. https://www.rnz.co.nz/news/national/503816/govt-confirms-it-... So completely uneconomic risk (plus other problems like NIMBY).