As an ex-controller, long out of operational positions, back in my day we generally knew about the approach ban but, to an extent at least, didn't care.
The equivocation comes from the fact that knowing whether a particular operator or type might be able to make an approach or not could help planning where to put traffic in marginal conditions. Knowing the RVR that would enable an aircraft to make or continue an approach was sometimes helpful also to understand who might want to start an approach when the weather update arrived. I'll be honest, too, that there were occasions when an inbound was five or six miles out and the RVR dropped I might be otherwise engaged for a few moments and unable to pass the new values until the aircraft was inside four miles. But, of course, all of this is just war stories from years ago, at an airport where the ILS was only Cat I at one end, it wasn't that busy and there were a fair few aircraft which were not fully equipped for AWO - times have changed in many, many ways - but I think the basic principles remain, pilot flies the aircraft and worries about whether he/she can start or continue the approach and the controller advises when the pilot can give it a go if they are permitted. But I must mention that I found the shifts where such things were going on to be some of the most satisfying.
Having said all that, I did have some involvement with the UK's foray into blurring these boundaries with the absurd 'absolute minima' procedure which, if nothing else, made it clear to everyone how many factors are involved in getting aircraft onto the ground in poor weather.