Even with 0% inflation savings do have inherent costs and risks: you might die before you get to spend them, they might be confiscated by some future dystopian state, or society might just get poorer and the money buys less in the future than it does now.
Most obviously there is the time value of money. Money by itself isn't useful, only the things you can buy with it are. Something today is more useful than the same thing in a year.
Economists often act like none of the above is true. They argue that given an improving world people would just do nothing, hoarding money in the expectation of it being worth more in a year. For as long as I've been alive the 2% target has been justified with this sort of nonsensical circular pop psychology, in which supposedly devaluing savings was required to manipulate the people out of their naturally zombie-like state (which if true would obviously mean the economy wouldn't grow, acting as a negative feedback loop that would then make it immediately untrue again). The existence of counter-examples like Switzerland did not bother any of them. Now we read that this wasn't even the actual source of the number, it was just plucked out of the air and justified retroactively! Not really a surprise given the weakness of the original argument.
Yes, savings should have a cost and/or risk associated with them. Furthermore, it’s insane to expect otherwise.