Won't happen as all the possible frequency spectrum to do things like this has been sold off to the phone companies.
ITV West from Ridge Hill is transmitted from a special mux that only contains ITV West SD.
It's a QPSK mux, with 10 Mb/s payload. ITV will only be using 2 or 3 Mb/s, so there is space
there to also carry BBC 1 West SD, but the Beeb have never appeared to be interested in the idea ?
Just a thought as with the TV spectrum being moved to free up the frequency for phone networks, wouldn't there be more frequent space and as Markymaek said there is a capability after all think its a bit unfair to pay TV licence when I have to stream my local news on iplayer. And that not being live as would be on BBC one so not exactly getting my local news when they are live, wonder why the BBC have never had an interest in this, seems strange as well when watching the titles for the 2 regions, Midlands today has Gloucester in the place names but Gloucester cathedral appears in the opening of points west and Cheltenham its in place names.