> Money is theoretically supposed to be a store of value as well, but it is not a good store of wealth, due to inflation.
Medium of exchange and store of value are the two main functions that "money", as such, can have, but it is misleading to say that money is "theoretically supposed" to serve both purposes. Any particular money is adopted with very specific purposes, and modern fiat money by design has a very limited role as a store of value, being intended primarily as a medium of exchange that is useful as store of value only in the short term (and only secondarily so, as utility as a short-term store of value is essential to utility as a medium of exchange) specifically in order to encourage investment in productive non-money assets as a store of value.
Medium of exchange and store of value are the two main functions that "money", as such, can have, but it is misleading to say that money is "theoretically supposed" to serve both purposes. Any particular money is adopted with very specific purposes, and modern fiat money by design has a very limited role as a store of value, being intended primarily as a medium of exchange that is useful as store of value only in the short term (and only secondarily so, as utility as a short-term store of value is essential to utility as a medium of exchange) specifically in order to encourage investment in productive non-money assets as a store of value.