Pumped hydro is just not a valid comparison. I wish people would understand that already… it’s only good for long term storage in certain key geographical regions. Its use case is very limited.
You don’t want to used pumped hydro for short term storage because the rapid cycling will drive up the maintenance costs. You actually hear about hydro power plants talking about installing batteries to reduce wear.
In these discussions please keep in mind that frequency regulation, short term and long term shortage are different applications with different needs. The costs for pumped hydro are generally reported with their target application in mind. It’s not as applicable to dedicated short term storage and certainly not applicable to frequency regulation.