But fiat currencies were designed to be inflationary which makes them shitty store of value. There is no point in saving in fiat today when it’s value will be lower tomorrow.

Exactly, working as intended.

You want people to hold real assets, not imaginary ones like a currency, because you want people to be invested in your economy. The only intrinsic value a currency have is taxation.

Currencies aren't supposed to be a good store of value, just a predictable store of value. Investments are supposed to be good stores of value. The government very much does not want people hoarding currency.

We don't want people just stuffing dollars in a mattress. That doesn't help either themselves or anyone else. So we encourage putting dollars/currency into interest bearing vehicles or real assets.

We don't want dollars to sit in hoards. We want them to circulate. If I can be without access to dollars for a while I can loan them to you for some enterprise. Then you pay me back more than I loaned you (and more than inflation we hope) because your enterprise created additional value.

If my excess money circulates I benefit from access to the things that money is used to build in addition to the interest I receive. Since I'm not a medieval landed noble my economic value isn't measured by the productivity of the serfs on my land holdings.

Most cryptocurrencies were designed that way, but some have a so-called tail emission making them disinflationary. One even has a completely linear emission of 1 coin per second forever since launch.

That doesn't help because inflation needs to be in tune with the economy, so somebody has to be able to adjust the amount. If the tail emission is too small then it's still deflationary. If it's too big, then there's too much inflation.

To adjust properly there has to be somebody who decides what "in tune" is. We're either back to centralization, or it's some sort of popularity vote which is unlikely to produce the right result.

It might be possible to have it self-tune to transaction volume, no?

It's not about the volume, but about the economy though. If somebody keeps sending coins back and forth between their own wallets, that's not economical activity.

Assuming there is a charge for transfers, that sets a minimum bound on the expected global utility of a given transfer, the sum of which, would intuitively be correlated with the size of the economy.