I can't speak for everywhere obviously, but where I work criticism is definitely passed on because I'm usually one of the people on the recieving end of the post mortem when a poor review comes in. I know that things have been changed based on feedback we've received.
I will agree though that sometimes, it's not acted upon, or, twisted to make it the fault of the staff on duty when actually it's a staffing or system issue that's the real problem, and that needs fixing but there's always the 'apologies and more training' response which pisses me off as much as I'm sure it pisses the customers off.
Thing is though, that so many people only review negatively, and that can give a skewed overview of the place. So asking everyone to review tries to combat this by encouraging happy customers to review as well as unhappy ones to give a more balanced view, we might have had 99 happy customers today, and one who wasn't, but if the one who wasn't happy is the only one to review then it's not giving a true picture that 99% of customers were actually happy and only one unhappy, which on balance means the place is a pretty good one.
We don't expect every customer to review, of course not, and I don't review every single time I'm asked, but I do try to, especially if it's been a good experience as well as if it's been a bad one. Unfortunately reviewing online is now seen as a blackmail tool by some, and most people do read reviews of somewhere before they stay/dine/buy to weigh up if it's worth it, so it's worth a business trying to even things out, especially when you're told in person how happy people are but then only the bad ones end up published for all to see.
I also like reading them, gives the opportunity to reflect on something not done right and a boost when something is done right. Much rather have a positive review than a tip tbh!