Fedimint is not a solution for anything. Doesn't add privacy, subtracts by adding counterparty risk. Maybe vaguely useful for poor connectivity times but honestly, you don't need much more than 56k dialup to do a tx on chain using neutrino/electrum SPV.

P2P payjoins would solve the fee problem tomorrow. Same as how batching solved the problem for exchanges.

Sidechains and altcoins do arbitrage the fee problem pretty good though, you can hold off on such a transfer a long time. Not sure if arbitrage is the right word since deferment is the main benefit.

Lightning is great but its poor availability (weak with bad connectivity) is very problematic. It's the exact thing that chaumian mints could resolve by allowing a deferment to settlement later, but I'm not sure whether they really do it better than an alt/side chain. Altcoins like Monero and Litecoin have practically zero counterparty risk.