I suspect that there are a reasonable number of schools who treat MAUW on these simple training aeroplanes as just a suggestion. They shouldn't, but it's also an aeroplane tolerant enough to deal with it.
Why is it so popular in schools? Mostly, I think, because it's so cheap to buy and run. But, in amongst that, it's got excellent handling, benign stall characteristics, a pretty good view out, very uncomplicated controls, and performance which if hardly sparkling, is almost always good enough enough. Plus, it's very cheap and easy to maintain, with a reasonably low fuel consumption.
So, at the end of the day, it's a really superb basic training aeroplane - if a bit limited in payload. So, lots of schools operate them, and you'd struggle to find many pilots worldwide who haven't flown one at some point.
Personally, I also think that it's the second most boring aeroplane in the world after the C172, but that doesn't in itself make it a bad aeroplane for most purposes.
G