In general, habits are hard to change. Muscle memory in athletes is hard to change. Processing ability is hard to change.
There's a list of starting QB in the NFL whose accuracy and ability to read the field unquestionably improved in the NFL. The list would include Steve Young (traded by his first team, "bust"), Drew Brees (first team drafted Phillip Rivers 'cuz they thought Brees couldn't play), Ryan Fitzpatrick (took him 5 years of playing in the league to crack 60% completions), Matt Stafford (3 years to crack 60%, 6 years to stay there consistently), Alex Smith (from "top 10 bust list" to solid starter - just took 6 years) - I'm sure I can think of others. Sam Bradford, perhaps. Then there are QB like Case Keenum, Nick Foles, and perhaps Mitch Trubisky who can have an all-world year with the right OC and talent around them, but regress badly when too many changes are made. Last, there are QB like Matt Schaub, Tony Romo, Aaron Rodgers, and yes, Pat Mahomes who looked very good once they started - but who sat on the bench 1-4 years before they stepped on the field as a starter. Would they have looked the same if they started right away? We'll never know.
Of course, there is a much longer lists of QB who had "steps to take" coming into the NFL and who failed to take those steps.
Allen is considered suspect by the "stats geeks" because unlike many of the other QBs named above, he didn't complete a high percentage of his passes in college. Ironically, the same stats mavens who claim to separate the effect of the talent around the QB from the QB's performance don't seem able to do this for Allen in college. Allen didn't follow the path of Russ Wilson, who actually changed programs from NC State to Wisconsin and saw his completions jump 15%.
The bottom line IMO is no one as yet has figured out a way to measure heart and determination and their impact on what a QB can become. As far as one can tell, Allen is doing all the right things - his offseasons include sitting on the beach and golfing, but also clearly include intense work on his craft. And he seems to come back better each year.
It's really IMO not worth getting in a lather about. Allen has already confounded most of his pre-draft critics who seemed to predict he'd have no success at all. Playoffs, Baby.
Either his heart and determination and intelligence will allow him to solidify his improvements, or they won't. I'm betting on the former, but if someone wants to bet on the latter they have some history on their side.
The other possibility is that if he keeps trucking linebackers and DLmen, he won't last in the league.
The Jets offense is looking like a hot mess.
The Jets defense is in the middle of the pack, which is actually fairly impressive given that they lost a couple of their best players and that their offense hasn't given them much help.