This simply isn't true, unbundled providers exist pretty much everwhere in the country and have their own equipment in the cabinet.
No, they don't. Some of them have their own equipment in the exchanges (and for ADSL that will include a DSLAM) but all the equipment in the new VDSL/G.FAST cabinets belongs to openreach. The LLUOs made it clear that they couldn't justify adding their own equipment to street-side cabinets.
So everyone with a VDSL or G.FAST connection is using openreach equipment and cabling to get to the exchange. At the exchange openreach hand over the traffic to various CPs (including BT retail) using their GEA product.