That what I did and allowed ppl todo back in GM days of 1991-1995, AD&D mostly, a little DnD 1st. Pick class, then 3d6 x6, done, off to the cave and fight the rust monster on the left
Though I did allow, after some fast deaths on appaling chars from players, decide to ease to roll 6x 3d6 and then choose what belonged to which stat and then pick a class. After all ppl are born with some stat distro and then pick what class they wanna specialize in while growing up, so class after stats made alot more sense to my players.
I do agree on a hard line, though it cost some players over that time and lack of progress(dying or players bailing/"backing out on" adventures I spent hours making) because of this cost the last players and the group closed. All to avoid the much worse power creep.