Pre digitisation, PBX's and exchanges were mechanical, they were huge, with limits on capacity, very labour intensive.
Also cabling plans never expected such a boom in demand, so your 1 line order, could mean extra cabling and additions to the main exchange, all taking many people and time.
Tech got rid of all of this, one person, can now look after several main exchanges, backed up with remote service centres... one fibre cable can carry 1000s of calls and internet traffic, its also very much more reliable.
A box the size of a small thin suitcase, can now provide 10k plus lines, which are all IP based.
Yes of course there was inefficiencies, in any organisation there will be but delays in getting a line was basically down to lack of capacity.
I started in comms as BT was formed, i saw the explosion in tech and the huge numbers of companies that went into telecoms, the waste, duplication, slope shouldering and shear incompetence was and still is mind blowing.
Look at Energy & Hinkley or Rail and HS2? efficient they most certainly are not.
BTW i'm not saying that privatising the GPO was a bad thing, probaly one of the few things that should have been but the idea it has automatically led to some explosion in efficiency is just plain wrong, its this thinking that has led to all the other privatisations that have fucked up the UK..
On the GPO, look at Hull? they weren't sold at the time, yet Kingston Comms became hugely successful, run by the local council... only fucked up when Prescott ordered its sale.
R4 have been running a good program on Thatcher/Redwood on how and why they privatised or imho, sold out the UK, as Macmillan said at the time "We are selling the family silver, once its gone, its gone for ever"