Let's try this and see if it makes sense. Are we all in agreement that Vince should see the field very sparingly if at all during his rookie year? Whether that be because his skills are not ready to be an NFL QB, you think he game is ready but you want him to sit for a year to get used to the speed of the game, or you just want someone else to be the whipping stick behind our OLine in a new offensive system that everyone will be trying to learn, whatever the reason, does everyone agree Vince should not really play this year unless it's at the end of a blowout game or he has just remarkable progression in his game?
That said, of course the fans patience with Carr is growing thin, I can understand to a certain point why it would be, but their impatience is going to be 10x worse with Vince here next year than without him. If Vince isn't here, if Carr and the offense don't have immediate success then people will be grumbling about it, but they won't have had a chance to see Vince in action at whatever team he ends up going to, so they won't have anything out of Vince to show that he is some great QB and their only options for running the offense will be continue with Carr or put in Dave Ragone. The impatience will be there, but no worse than this year.
If the Texans do draft Vince, every single incomplete pass that Carr throws will have a lot of fans booing and calling for Vince, which will either undermine what little support the fans do have for Carr and draw them away from the games, or it will force the Texans to put Vince into the game long before he is ready to. The fans will have so much less patience for Carr and be calling for his removal from the lineup long before he should be removed, and will hold Carr and the rest of the team to much higher expectations than they otherwise would. I think much of the problems that would be happening would be everyone else on offense adjusting to the new system as much as it is Carr's fault, and when Vince steps in personally underprepared and with an offense that still isn't running our system correctly, that will only make things worse with the team. Many fans that didn't overly want Vince to begin with will be upset at the decision, and many of the fans that did want Vince will just accept it as part of his learning process and be content with our team going 2-14 again because at least Vince is getting his time, and Vince will be thrown to the wolves before he is ready and probably slow his progression as well.
Now what happens if Carr ends up turning it around and thrives in our new offense? Carr keeps rolling, the offense is putting up a lot of yards and points, team is playing well and winning. Then we have to make a decision about the future QB situation of our team. Either we are going to have to trade Vince Young, lose out on the $20+ million bonus and $6 million annual salary we've already paid him to do nothing for us and take an additional cap hit for trading him, or else we're going to have to move Carr and start our offense over again with a new QB. This is a lose-lose situation for both QBs.
Going back to the original premise that Young should not be playing much if at all during his rookie year, for this next year alone, drafting him adds nothing to our team. We have the #1 pick in the draft, and we add nothing that helps our team improve for the upcoming season other than a backup plan at QB. Then since we have Vince, people are going to demand that Carr leads the team to an 8-8 record (or some other arbitrary lofty goal) and puts up X stats or else they are going to complain and boo and demand that Vince get put in. So rather than helping Carr improve and better his chances of providing a winning product with the top pick in the draft, we add nothing that helps him along this path, and if anything the fans scrutinize him more severly for any mistakes that he makes along the way and it diminishes from their support of him. Many of these people would probably still complain at Carr if he put up numbers like Matt Hasselbeck did this year (3459 yards, 24 TDs, 9 INTs) in a Pro-Bowl year, because they demand so much more out of him in order to keep him in front of Vince.
I think this creates a situation that will leave many fans unsatisfied no matter how well Carr and the Texans do until Vince gets on the field, and if Vince does see playing time then they'll be happy with less-than-mediocre play because it's their hometown hero Vince out there. They will demand so much more out of Carr to be happy with the team than what they'd demand out of Vince and likely create unrealistic goals for the team in order to not be disgruntled with it. In my opinion, this is setting Carr up for a failure, whether it truly be a failure on the field or just in the minds of some fans that want to see Vince no matter how much Carr produces. I don't see drafting Vince as being a good situation for the team, it doesn't help the team get better around Carr, it creates a rift between many "fans" and the team, and it sets Carr up for failure (moreso in the minds of the fans rather than on the field, but lack of support and criticism will eventually impact his play on the field) and in turn sets Vince up for the same failure (more of actual failure to produce on the field as he's put into games too early in his career), and it absorbs a lot of money that could be used to improve some other area of the team while not adding anything to the existing offense (or defense) to make those better.