In an ideal world of course it would be left, but there's conflicting priorities and IMO the housing crisis is more important than saving golf courses and maintaining the property prices of those who live in the Green belt.
Come on, now, that's just silly. The greenbelt was created for reasons that still apply today. And most greenbelt that gets the go-ahead for development is agricultural anyway (the loss of which means we need to import even more food, with the accompanying food miles implications)
The 'Housing Crisis' isn't solely about the number of dwellings that there are in the UK. The main problem is the unaffordability of housing (to buy or to rent) driven by a demand for housing that is massively swelled by those buying property as an investment to rent out. It's this that needs addressing - and especially the selling to overseas investors.
There's a lot of brownfield sites (and 'landbanked' land) but it's generally unattractive to private developers because there's remedial work required and they're generally not in leafy countryside where they can charge a premium and hike their margins.
Giving greedy bastard private developers carte blanche to concrete over greenbelt is wrong on so many levels, and will do little to address the fundamental issues of affordability (the tactic of just trying to add more and more supply into the market to drive down prices has failed for years).
The way to tackle the housing crisis is a massive programme of social housing (at least 250k a year, ideally more). Build on brownfield sites - even confiscate land 'banked' by developers' to build on. Rent them out at a price that's non-profit to subvert the private rental market to bring down rental prices generally. That in turn will lead to a lot of private landlords selling-up, which in turn will gradually lower/stabilise house sale prices.