Imagine a world where politicians (or their descendants) couldn't abdicate except though untimely death? Arguably they would take their profession much more seriously, like a monarch.

British Members of Parliament are, in fact, notionally forbidden from resigning. There is deliberately no provision to "step down" as the representative. Historically there were cases where people probably did not want to be made MP.

Today, however, in practice you can resign. What happens is you tell the people who look after day-to-day business in the House, and they arrange for you to be offered a job by the Crown which you then accept. Obviously the people's elected representatives can't be the Monarch's employees, that's no sort of democracy -- and so this immediately terminates their membership of the Commons (fresh elections will be held some months in the future to replace them) and immediately the same offer can be re-used. The "jobs" given aren't real jobs, one that's used is Crown Steward and Bailiff of the three Chiltern Hundreds of Stoke, Desborough and Burnham. https://en.wikipedia.org/wiki/Chiltern_Hundreds

Basically the wooded hills where I grew up were once bandit country and so the Crown used to pay somebody to sort out the bandits, the job still legally exists, but today the sort of bandits who live in those hills (bankers, executives, sometimes the Prime Minister himself) would need more than merely a "Crown Steward" to sort them out.