We can and do, they're called stablecoins. It's not possible to send fiat around unless you digitise it first, and this needs to be done in such a way that it's impossible to mint more in the process and such that this is verifiable by everyone - hence (most) stablecoins.

Edited to add: Also XRP is used as a bridge-currency to automagically do what you described, but with XRP in place of NANO. This is a product that due to regulatory uncertainty is not widely used yet, but it is still offered to, and used by various banking and payment firms who have signed up for it with Ripple. It's been hampered by the SEC in the US, but is still used elsewhere.