We seem to be talking at a slight cross-purpose
.
As Andrew explained, to instigate a USO-satisfying service in an area you are correct. However, the result of that is that if it is landline based then that landline service can be provided to all other people covered by the same aggregation point (for FTTP) or FTTC cabinet by any provider of their choice 
Sure. There are even incentives in that direction: there is "assumed aggregation" of demand, so if there's a cluster of 10 houses, and only one of them requests USO, then it's assumed that all 10 will want it at some point and potentially £34,000 is available to connect them.
But equally, BT could just give the one property an EE SIM and an external antenna, if that will do the job.
There's no way that EE will put up a new 4G mast, demand-led from a cluster of 10 houses. But if there's existing 4G coverage (including the new shared rural 4G network), or it's due to be delivered within 12 months of the USO request, BT could use it.
The USO-instigated service becomes available to all, and they do not have to get it from BT Consumer or Business.
But at that point, they're no longer ordering a "USO" service. You said originally:
"I think you will find it [the USO] applies to all ISPs (Technically, in Ofcom-speak, Communications Providers - CPs)"
But it does not. The Universal Service Obligation applies only to BT and to KCOM. You cannot claim connectivity under the USO from anyone else.
If your neighbour ordered USO at some time in the past, and as a result you have FTTC or FTTP available at your property, then happy days - you don't need USO.