First point - granted. But if no private company has picked it up in the meantime, it's probably because it's just not profitable.
Last train driver strike, the signallers went out on strike too in sympathy. It's not as simple, once things are unionised.
My sorting office is my local branch. Which is 2 miles away (20 was hyperbole for effect), has no parking, has a local glut of traffic wardens even on weekends (precisely because there's no parking) and is only open between 11am and 4pm Mon-Fri and 9-11am Saturday. Guess when the world and their brother decide to collect their parcels, needing to have their ID checked, etc. forming more than a 2-hour queue?
Your options (according to the little note they pop through) are delivery to another address (same restrictions), redelivery to the same address at the same times (and a maximum of twice before they give up), or collection at the times above. That's it.
And that's if they are post-office parcels and not ParcelForce - who have similar but different restrictions and locations - or some random third-party courier (who are generally even worse and one of them is 8 miles from me and charge for redelivery!).
And I guarantee that you've heard of the town I live in, inside the M25, serviced by several underground stations (also between 1-2 miles from me) and lines.
Amazon lockers? Last time I used one, it was in a petrol station late at night with no security and nobody around. Sod that for anything of value.
AmazonCollect? The last time I went to a newsagent that was supposed to be part of that, they knew nothing about it and didn't have my parcel and the other time I used it, that newsagent refused to accept my parcel for Amazon Return that Amazon themselves (on the phone) had said I could do from that newsagent.
By comparison, I'd rather pay just about anything to get someone to come to my house of an evening with the parcel or - better - ring first.
In the last year or so, though, I've been at a workplace that is manned 24/7 and allows staff to have personal parcels delivered there. Solves no end of problems, but no thanks to Amazon, the Post Office or any delivery company. And we still get hassle because some things companies will refuse to deliver to business premises!