I think some people are conflating Post Office and Royal Mail. These are two separate organisations, Post Office is a wholly government owned corporation and Royal Mail is now a private company, although one provides services to the other. The PO sells RM products and collects revenue, e.g. stamps and parcel services, but has nothing to do with the collection, sorting and distribution of mail.
Post Office services are mostly provided on a franchised basis, i.e. at counters within convenience stores etc., with only a few ‘Crown’ offices operated directly by the company. I am not altogether certain what government services are available through the Post Office as I do all my business online these days, but at one time you could tax your car, buy Premium Bonds, buy a driving or television license, obtain a passport etc. and collect your pension or other social benefits over the counter. Maybe you can still access all of these government services at a PO, especially a Crown office, but I won’t be making a thirty-mile round trip just to be told that I have to do these things online!