There are other strands to the BT/OR issue, that aren't just to do with OR, and acccess to infrastructure.
I'm willing to bet that at least 50% of most customers (by which we mean end users) complaints as regards Openreach are based on some variation of the following scenario "We'll tell OR that this needs [activating/repairing/doing.] We'll let you know when they decide to do something. They say it's delayed. We can't get any information as to why, when it''ll be sorted, how you get it sorted. they will only speak to us, not you, and we can't push the issue with them." The complete lack of any accountability from OR for delays, timescales, information, anything.
Admittedly, this is at least somewhat down to the service providers, who seem to, as a general rule, be unwilling to try and hold OR accountable for their actions (convenient scapegoat ahoy) and hide behind the "we don't have any access to OR" rules, which leaves consumers feeling utterly powerless, when the company that's actually going to do the work isn't even contactable. At least with other utitlities where they subcontracted out, generally the contract means they actually have a measure of control. If the ISP's have any control, they mostly seem to be declining to exercise it, because it's no skin of their nose if OR screw up, as they can just go "not us, guv."
Divesting BT of OR may or may not help with issues of infrastructure access, investment and upgrading, but it probably won't fix the other issues with the system.