Dont forget this is a two-way street; the UK have introduced a visa scheme for non citizens entering.
It's not quite a two-way street... 🙏
The UK scheme that you are thinking of is called ETA. It's not actually a visa. It's a passport pre-registration like the US ESTA, explicitly for people who do not need a visa. (The difference between "a visa" and "pre-travel registration of your passport with a visa waiver" is important, but it takes quite a long time to explain why.)
EES has no UK equivalent because the UK does not take biometrics from people arriving with a visa waiver. However, next year the EU will also launch ETIAS, which is indeed a very close equivalent to the UK's ETA. At that point, the EU will have two sets of hoops to jump through (EES and ETIAS) while the UK will have only one.
It is important for UK people to understand that this is not "revenge for Brexit" — indeed, the UK was involved in the preliminary discussions around ETIAS and EES when it was in the EU, although since both concern the Schengen area, neither the UK nor Ireland had a big part in the actual design of the systems.
Of course, the knuckledraggers are already writing "What about the illegals hur hur hur" under every online story about EES, and will also write "We should do the same to the EU" under every story about ETIAS (which, as you noted, the UK is in fact already doing).