There is an argument that the funds being ploughed into competing fibre networks (in London near me OR is likely to be overbuilt once in many areas and twice in some, not counting Virgin) would be better spent on a national infrastructure that could have greater reach due to the removal of overbuild.
The trouble is, in areas covered only by Openreach, there is no business case for them to invest. Existing customers may have a poor service, but they have no other choice. If Openreach roll out FTTP then every customer gained on FTTP will be a customer lost on copper; there will be a few who pay a premium for ultrafast services, but most won't, so there is very little revenue gain.
Hence it needs the likes of Virgin and Cityfibre to give them a kick into action. Rolling out FTTP to regain lost customers back is gained revenue.
You're not going to get national coverage from those though. Even Cityfibre's long-term ambition is for only 30% coverage. They will cherry-pick the 30% of the UK which is cheapest to build to, and they will compete by undercutting: regulated pricing means that Openreach can't sell below the price set by Ofcom, and this is explicitly so that other operators have an incentive to overbuild.
Sure, the government could pay to build a national network. But what then? Will they be left holding and running a national network? Or will they gift it to Openreach, which is basically a gift to BT shareholders? Or will they lease it to Openreach, which is really no different to Openreach borrowing the capital and investing themselves? Or break it into franchises, like the great success of national railway?
At least Openreach *are* building out fibre now, much faster than any other operator. Cityfibre recently announce 500K properties passed in total; Openreach build that much every 3 months.