this is where visually "more simple" games like Megaquarium, Parkitect and Two Point Hospital actually do a lot better. Problems are immediately visible on screen in the aquarium/park/hospital itself, not in the UI or in text messages
Different is not necessarily better.
You happened to list three games with distinctly cartoon style, which conflicts less with arbitrary floating icons. You can add Parkasaurus, Flotsam, Oxygen Not Included and many others to your list of games that do this kind of thing well - they all happen to be quite markedly stylised. There are examples of non-stylised games that do the visual indicators thing - Cities Skylines does it, for example.
Notably, Rollercoaster Tycoon doesn't use any of your suggested visual indicators, beyond the same kind of stuff done by Planet Zoo/Coaster - tired guests having droopy walks and suchlike. On the UI point, Democracy is a management game that works entirely through UI, and I wouldn't go so far as to go it is 'better' or 'worse' than other ways of communicating the same information - just the decision they made for the game they were building.
The Cities Skylines example is also interesting, since the icons easily distract from the city itself - buildings often less visually important than any floating symbols. Seems odd to me to spend a lot of time making a game look good and then litter it with symbols. Possibly why this is more common with less overtly realistic-looking games.
The furthest I'd go is that UI-only tends to read a little more 'hardcore' than friendly visual indicators, but I'm still sure that different is not necessarily better.
2) the management aspect is built on identifying problems that consist of statistic bars whose levels need to be improved which makes solving the problem not very satisfying
Do you have an example of a game that does this well, for you?
I have to say that playing the beta, only a tiny fraction of my time was spent filling bars - only in the terrain set-up and adding enrichment items when they are researched.
Otherwise, all the time was spent doing cosmetic things to make the zoo look the way I wanted, changing stuff around to optimise travel time for staff/guests/animals, and managing breeding programmes - moving animals around to optimise genetic potential.
I suppose I spent a fair amount of time messing with 'Compare Mates' to make the most of the genetic diversity I had, but this was still a very small part of time spent.
An example would definitely help understand what you're imagining.