I have followed UP for my 2 and tbh I am very very glad I have.
Imo, UP isn't about letting the child doing whatever they want (As far as I know AK has never said that at all). It's about:
1- not using punishment and rewards as a one fit all solutions to all situations and,
2- when something happens, start with the assumptions that the child hasn't done anything wrong.
So that means that if you see a child hurting someone you will do something about it but if you hear some screams in the room next door, you don't automatically assume that your child has been naughty and hurt the other child.
It also means that you don't use fear (of the punishment) to keep a child in line, nor bribery (because that's what star charts etc... are. If you do X, you will get a sweet type of thing).
Interestingly enough I actually had no choice in doing UP because with dc2 (and to some extend dc1), punishment or reward never ever worked. Punishment just meant a child who was distressed, upset but had no idea of what he had done wrong. rewards, well he just didn't care what so ever.
The only thing I have consistently done is the 'going into your room to calm down' with the understanding that the child can come out at any point, whenever they feel they are calm enough again. A very necessary safety feature because of dc2 lashing out in anger on a daily basis.
I found that it worked for us because:
1- it made me explain, take time with dc2 to explain in words he could understand why x wasn't Ok to do.
2- It didn't say 'this child is naughty and is choosing to be like this/to hurt people etc...' but 'this is a child that has a problem. How can I help him?' The problem quite often has been plain education (ie he hasn't learnt yet that ....).
Moving on a few more years from the toddler times, I still use the same approach and I am very glad that I have because dc2 has been diagnosed with HFA.
So in effect, a lot of the techniques that I had put in place were actually exactly the ones I needed to have to parent dc2 effectively (and tbh, if this worked with dc2 with HFA, then surely it was going to work with NT dc1?).
One last word, there is a book often proposed as a fantastic solution to behaviour/parenting issue on MN. This is the How to talk to children. Tbh, their approach is my book along the same lines than UP. It's quite practical when AK goes into the reason and the philosophy of it and very little into the how. But they aren't that different.