I think it's just as likely that Allen sees a defense that is built to win now and an offense that is missing some key pieces. Fill those this season with rookies ready to start and this team can catapult into a serious NFC contender.
Very likely they can fill LT and WR in round 1 and still come away with a viable developmental QB in rounds 2 or 3 without much drop-off.
If Allen is positioning to make a move up for a first round QB, Pickett is widely considered the most ready. With the likely capital it will take to move ahead of other QB needy teams, going to lose a lot of value in the sort term as well as the opportunity costs of getting better at OL and WR with 1st round talent. Not saying it can't or won't work, but it doesn't look as favorable as other options, to me.