It's not like that at all.
If you want to argue that one can't define value then I am out.
If you admit "value" has well understood meaning then utility function of wealth is just how much value one can derive from it. We usually measure wealth in money for convenience. I really don't know why you are so against it. There might be a lot of nonsense associate with it but the concept itself is pretty simple and useful.
Precisely. Like when a priest says that "love" is "god" and "god" is "love".
Plenty of our language is deeply unscientific.