Good size and build, arm strength, athlete, scrambler/runner... you just described a bunch of stats. Lots of guys have failed as NFL QB's with those stats.
As far as improving as the season went along, I will have to take your word for it because the game logs don't support your assessment.
First, his last two games that I mentioned weren't two good games. It was one good game with 400 yards, 60% completion rate and 3 TD's combined with one bad game with 198 yards, 33% completion rate and 3 TD's.
And even the good game was subjective because they were down 28-12 to Vandy when he started slinging the ball all over the field, throwing for 215 yards and 2 TDs on 10/19 attempts in the last 12 minutes of the game. Up until that point in the 4th quarter he had 185 passing yards.
In the FSU loss as his final collegiate game, here are his stats through 9:25 in the 2nd quarter: 5/7 151 yards 3TD 1INT. Absolutely brilliant.
For the rest of the game he doesn't make a completion until their final drive in the last two minutes, where he gets bailed out on a 4th and 18 with a PI call, makes three decent throws to get into the red zone, then proceeds to have three straight incompletions to lose the game by 7 points.
Second, in 3 of his last 5 games, he had a completion percentage below 50%. This was out of 88 pass attempts in those games, so it's not like the game plan was to limit him in this area. In his last four games he averaged 30 pass attempts per game, yet only got above 200 yards once. Again, he isn't in a run heavy offense that is attempting to limit is throwing.
All this to say that while he may have been seeing reads better and was responding to coaching, his play was inconsistent throughout the season and definitely not on an upward trajectory, he was also wildly inconsistent within games as noted above.
That being said, I don't see anything about how he plays that isn't correctable with coaching and experience. He doesn't look to run first but maximizes designed plays. Has all of the physical attributes as you noted above. But he is about as raw and unproven as any QB we've talked about in the last several years being a potential first round prospect, and could absolutely set himself up for next year's draft by getting another year of coaching and development under his belt at Florida.
I literally said that any QB taken is a risk, so not sure the need to counterpoint me. I'm simply saying there are much more NFL ready QB's that will be available to the Texans at 2 and 12 if that is the way they want to go. They don't need a project, despite all the "potential", "upside" and "high ceiling" adjectives that may be used to describe him. In my opinion, because I don't want to confuse anyone as to my role in the Texans draft this year.