How thinks this is a bad idea?

I really think it should be your FH who tells them, and it should be immediately. Judging by what you said, this has already gone too far and they really have their hearts set on it. They may already be planning how to redo the house and that sort of thing. If it's not handled properly it will hurt their feelings and they will take it personally. I really believe their son should thank them profusely but firmly say he wants to start off his marriage alone with his wife. He wouldn't want to live with anyone else at the beginning - it's not just them. If you say it they will think you are the one who doesn't want to accept their very generous offer. They may always feel you were the one who rejected them. Forgiving their own child is easier. These are the things some people never forget and you wouldn't want it to affect your obviously very good relationship with them.
Good luck.

No question, it's a great way to save money-and money is what a lot of couples end up fighting about. Family is the other big the couples fight about. Weigh your options-but it sounds like you already know that you don't want to live with them, so just privately tell his mother or father-whichever you have the better relationship with that a new marriage is hard enough to adjust to, and the two of you are ready to make that commitment, it wouldn't be the same if you had parents there to curb your lifestyle. They were newlyweds once, they will understand.

I live with my FIL's now. DO NOT DO THIS!!!!!
I went from liking them to hating them. We moved in because we were having money trouble at first because will I was pregnant my FH lost his job. We figured okay well once you go back to work this would be a good opportunity for me to finish nursing school and for us to save for a house. BIG MISTAKE!!! Anyone who knows me can tell you all the depressing posts I have lately because they are driving me nuts. You wind up not saving money because you spend it on going out for the day just to stay away from them. I have spent many of days wishing I just toughed it out until FH got another job and stayed in my own apartment.