Hopefully remote working will take some of the pressure off of the city because it really does feel overcrowded. Although personally I probably would still stay near London given it's both where I was born but also having access to international food and Heathrow are quite important as a third culture kid. I've considered moving out to somewhere much leafier but losing access to decent Asian food might be my undoing. That said, I hear Liverpool and Manchester are not bad in that department...
I think your proposal is correct worldwide; it's not a UK-only problem. Unfortunately, it looks like humanity has not yet invented a successful economic model that doesn't require a cramped megacity (with a huge income inequality within) or stealing from other countries (see tax havens).
Ironically, this would be aided greatly by investing in public transport. Andy Haldane gave a great speech about this at the Sheffield Political Economy Research Institute in 2019 - the most salient bit is from page 37:
https://www.bankofengland.co.uk/-/media/boe/files/speech/201...
Excuse the snip, highlighting PDFs is hard, but here's a key-ish quote:
> ..a measure of the “effective” working population. At peak times, the effective working population of Birmingham is perhaps 50% smaller than its measured population due to poor transport infrastructure. This helps explain why Birmingham punches below its demographic weight
Virtually all UK cities suffer from this. The problem, as ever, is a lack of investment and too many cars.