Another one of those idiotic decision which has nothing to do with programme presentation and everything to do with politics. The programme works fine where it is so lets make it difficult by moving it to a place where there's no readily available studios for it

Drives programme producers mad
There's no way they've just decided to "move" the programme without actually thinking about where it's actually going to come from. The discussions of possible studio options/ideas on this thread are only happening because it hasn't been publicly announced yet. I don't think anyone's actually under the assumption the BBC are only now starting to think where it could potentially be shot, or are blind enough to have announced the show is moving without first checking that there's a suitable studio/space it could use.
We also don't know whether the show has been working "fine where it is" (as you word it) from a studio sharing perspective. Yes it works on screen, but it's actually a big job to re-set every day for the One Show and then back again by the next day. I know other productions do it, but the BBC might have decided it would just work better to have a permanent standing set for Morning Live now they're committed to keeping it long term, and there's a space in Salford which has been earmarked for just that reason. It could be to allow for rehearsal time, or pre-records, or a whole host of other reasons.
Of course, there's always a chance it's only a political move. But I doubt even that wouldn't be done without first giving some thought to practicalities.
The Beeb is so large sometimes you get cases of split brain. Don't exclude the possibility that BBC Studios Productions (who produce Morning Live) may have been thinking about this for a while but are still at high level discussions. I guess it depends on desired timeframe and whether budget is available as capex or opex. Whatever happens, it's encouraging news.
"
Based in Salford" has scope for interpretation. The press release specifies a timeframe of 'January next year' for Morning Live starting to come from Salford, so there's options.
Alongside in-house facilities, Salford has flexibly used Dock10 since day 1. Childrens studios are homed in HQ5 (CBBC and CBeebies presentation, Newsround,
Bitesize Daily from HQ7 and Live Lessons - though some also came from Manchester Studios, the old Granada complex on Lower Byrom Street). And not forgetting Blue Peter (HQ7/HQ3). HQ7 has become a regular studio for Final Score / MOTD. Dock10's also going to be used for other output this year. BBC and Dock10 have history!
One small Sport studio in Quay House was recently fitted out for VR, but I'd be very surprised if that ended up shared with daytime. The Breakfast studio might be more appropriate - a decent space, much of it is unused, probably due to shape and current set design, but that's also an opportunity. Either way that set needs an update and new kit. It would be very good to see a refreshed look for the Breakfast set which could accommodate Morning Live if they decided to hot-seat.
As it stands, the major infrastructure, bar the aforementioned studio, was installed when MediaCityUK was built, nearing a decade old. I'll be interested to see what happens, particularly as Tim Davie's speech last week included renewed emphasis on more and new programmes originating from Salford, and an increase in staff and budget for regional investment.
https://www.bbc.co.uk/mediacentre/speeches/2021/across-the-uk