[Stooky Bill]

BBC already has a special studio in London for shows to air on 5 Live - considering every BBC local radio station is connected to the BBC network, I am surprised they haven't bothered to use them to provide content to network BBC Radio - BBC Radio Wales studio is used for the early weekday breakfast show on Radio 2 as an example

It probably happens more than you think, for example Petroc Trelawny on Radio 3 does his show from BBC Cornwall in Truro. 6 Music have used local studios when they've been doing a live event of Record Shop Day. 

One of the problems is that local radio studios aren't that well equipped for network shows, and exist on their own system, often the presenter will be in the local studio and everything else comes from London. 

Programmes like Radio 2 Early Breakfast are from network radio studios, full studios designed for broadcasting in the main networks. The nations have them along with Birmingham, Bristol and Salford.