He's not a one trick pony, but he's done stuff like this before (multiple times even I think), where he'll string together enough good games (with some real "whoa" ones), that it completely fucks up the team, as they think "oh well maybe he'll be the answer at QB" or they had a young QB they were priming to take over and then he basically ruins them and the team is never confident in them again. But if they stick with Fitzpatrick it won't last. He's like a more consistent Rex Grossman, where some games he puts up numbers that look like he's a top tier QB, but then he'll have games where he looks so bad you wonder how he's still in the league (6 INT game against the Chiefs a couple of years back).
Frankly, he's about the worst thing to happen to the Bucs as he's not the long term answer, so he'll holdup Winston's development. Heck, this year, if he keeps the starting job, he's stalling Winston and this offense getting in sync (they'll have to fret on how much is the offense, how much is Fitzpatrick, and that means the offense is going to have issues moving to Winston). Even if Fitzpatrick keeps playing well, I don't see the Bucs going "yeah, let's ditch Winston and roll with him" (like, even for most of the season unless its at the level he's been at the first two games), so he'll effectively end up wasting a year of the team unless he plays poorly and Winston steps in and plays well. Their best bet would be if Fitzpatrick is still playing good, to trade him to some team that is playing good-great but really lacking at QB. But the thing is, I don't know who that would be. Maybe the Steelers? Say Big Ben has an injury and will be out for several games, and if he then retires this year, they could roll with Fitzpatrick while they sort out their QBofF. Maybe the Broncos if Keenum starts playing bad but the defense is playing great.
The market for Fitz is gonna be low, because he's not the long term answer, and a lot of teams have their QBotF, and even their plan for keeping them on the bench to sit for awhile if that's their plan. He's old enough that no team is going to consider him for more than the backup or a single year deal. The Bucs might want to keep him as the backup, but there's a high chance it causes drama and problems, which can sink the team. I believe the Bucs are fairly young, and if they ruin the team trust, I don't think they'll get it back, so they could end up squandering having what looks like a franchise QB in Winston.
If Fitzpatrick keeps playing well, I could see the Raiders trading Carr away (maybe the Giants if Eli retires) and then signing him while Gruden plans on drafting his QB (I don't think Carr is).