Depends. Several central banks are working on exactly that, see for example the recent speech by the FED and the whole GENIUS act regulation framework.

But to be honest where I am (northwest Europe) we already have subsecond person-to-person transactions via the normal banking system, no matter which bank the sender and receiver use. So stablecoin-ifying the Euro wouldn't make a huge difference. There might be more to gain if the region doesn't have that kind of payment infrastructure yet.