Because of the importance of driving in the US (right or wrong), drivers licenses are used as the primary identification document. It looks like there’s a similar use of the DL in the UK for buying tobacco.
In the US, you need to prove both residency and identity. To prove your identity in the US, many people don’t have passports, so they bring a tranche of documents to the DMV office. To prove residency, we typically bring utility bills, leases, etc. Usually people prefer to go in person so they don’t lose these documents and get feedback if they don’t have the right stuff.
It looks like in the UK, since driving licenses are administered nationally, you don’t have the same patchwork of 50 different organizations with different requirements and rules, and the process is much simpler.
I haven’t been to a DMV for 10 years. I can renew vehicle registration, renew my license, and so on online. When I bought a new car, the dealer handled all DMV stuff like getting plates.
I’m supposed to be due to get a new “enhanced” license that is good for air travel within the US, but I have a number of other documents (passport, global entry) that serve the same purpose so I avoid the DMV as much as possible.
In my state the DMV is probably worse than a checkup at the dentist, but not as bad as a weekend with the in-laws.
If a person does not (and does not want to) drive, how do they identify themselves? Where I live, everyone gets a government issue ID card, and the ID number is the citizen's primary key. Our government is still largely paper-driven, but there's little you can't get done if you show up in person with your national ID.
You hit uppon an important difference between the US and most of Europe/the UK. An system for tracking who your citizens are. In the Netherlands, where I live, the municipalities cooperate to keep track of all citizens, and their address (or lack thereof). This means that you never need to convince any beaurocrat that your identity exists. You might need to authenticate that you are indeed who you claim to be, but that is normally trivial (Show government photo id).
This simplifies the process massively.