What caught my attention was that the first-class mail rate in the UK is £1.35 which is about $1.70 at current exchange rates. In contrast, in the US a first-class stamp is $0.68 (I buy forever stamps in bulk so I was surprised to discover it had gotten that high). The USPS really is a bargain.
I think though, that the percentage of USPS first class mail delivered in 1 day (including Saturday) is probably pretty close to 93% since a significant fraction of mail will be within narrow regions (I would guess that the DC–Boston area itself accounts for at least half of first-class mail).
Back in the Netflix DVDs by mail days, it was rare that it took more than a day for the DVD to get to or from the Netflix warehouse (when they started shuttering warehouses in the last few years of service, that went up to two days each way for a DVD from Chicago to Columbus, Ohio).
I’d also point out that mailbox pickup in the U.S. varies by the mailbox, but many of the ones near me have late afternoon (3–4p) pickups and if I go to the mailbox by the local post office it’s 5.30p. I can even take it to the downtown Chicago post office for a 9p pickup.
Yes, Royal Mail tends to be far more expensive than USPS for letters and smaller parcels, including internationally (e.g. UK to US costs far more than US to UK), but they have relatively reasonable pricing on medium-sized parcels in my experience.
It definitely is apparent which is the private company based on their pricing schemes, even besides the more consumer-facing UK Post Office locations that are almost entirely franchised and often operate as a small convenience store, etc.
The prices have been increasing above inflation for years, but especially in the last few years - e.g. in 2001 a first class stamp cost 0.27 GBP (0.49 in 2024), and even in 2019 in was 0.70 GBP (0.86 in 2024).
Postcrossing maintains a list of international postcard costs by country. Going by cheapest for food, the US is #20, UK is about #100. Bahamas is the cheapest.