The only game in town....
The reason BT has a monopoly in rural areas is because the other players do not deem it worth their while to unbundle the exchange. It is precisely because BT was a monopoly that it had the Universal Service Obligation for providing phone lines.
Other providers prefer to cherry pick the most profitable areas, leaving the remainder to moulder away. Competition only tends to benefit the urban areas who get increased choice. Rural areas are left with the only provider who will provide a service, and it took a long time for that to arrive in the first place! There are still not-spots which are not able to get ADSL at all.
You see similar problems in poor urban areas which food retailers have abandoned which increases the costs of shopping for those who can least afford it.
The original point of monopolies (as awarded by governments) was to provide security to an investor to make them prepared to invest for something other than the short term. Why would BT spend millions installing fibre optic across the country if they immediately had to unbundle it to all comers?
Either offer them a monopoly for 10 or 20 years, to get the fibre installed, give all players in the market a universal service obligation (unbundle one, unbundle all) or, decide that the national infrastructure requires investment by the taxpayer, and create a national telecoms grid, owned by the state, and offering wholesale access to all players. That way, we might get the fibre that is needed.
The benefits of faster access to rural areas can also help on a national basis - teleworking becomes more practical if you can get 100Mbps to the office - this reduces congestion, carbon and many other things deemed to be to the public good, but not necessarily adding to the bottom line of BT or any other telecoms provider.
After the infrastructure is in, we have the potential to privatise another utility, but at least we have it.