Actually that is a pretty short sighted view. There are more factors that go into team roster decisions than that. I do agree with your general statement that it would appear that Cleveland would continue building its team through the draft rather than trade for an aging QB. So at first blush, most people would expect Cleveland to be excluded from the list of current teams who would be interested in taking on Romo.
Then again, the NFL is also a profit oriented business. The Cleveland fan base has to be totally sick of the Browns and their pathetic performance for many years now. Moreover they have existing players who are trying to escape in a mass exodus. They are not able to compete for free agents because of their situation even if they are willing to overpay to get them.
Them drafting a QB at #1 overall will not likely pay dividends for several years, if at all based on their past history. If Cleveland traded its first round pick to Dallas for its first round pick and Romo, they would have Romo elevate that team to a very competitive team (for a very favorable salary cap number), draft a QB with Dallas' late first round pick, and have that player locked up for 5 years on a very favorable salary cap number. In some sense Cleveland drafting high every year is a bit of a curse because of the cap implications of a pick that high.
There are a lot of different scenarios where Romo could find a home. Some of them are not anticipated in the same way that no one expected Bradford to go to the Vikings. If you value Romo as a francise QB and think he can play out his contract (some will and some won't) then there will be more of a market for him than you think. I think it is probably moot though, because I think the Cowboys still view him as a franchise QB and better than Dak so they won't trade him anyway.
There are a couple of issues here:
1) Romo doesn't make Cleveland very competitive. They have way too many holes that are going to take a couple of offseasons to fix before they could be considered competitive. So that's one big reason they would have no interest in Romo.
2) Romo's cap number would be $14MM next year based on his current deal. If the Browns take Watson or Kizer with their first pick next year, his cap number will be around $5-6MM. So for at least the few years Romo would play, no his cap number is not as favorable as if they took their next franchise QB in the draft.
3) Three, they've brought in baseball people to bring analytics into football. They've been about accumulating as many high picks as they can get. They aren't about to turn around and trade a high first round pick for an aging QB coming off two injury plagued years.
The Browns simply aren't in the position where taking Romo on would make sense.
In the end, this really isn't my overarching point. I think there is definitely a chance Romo could be traded. I do believe someone out there might take a chance on him. Where my issue comes in is the belief that he's uber valuable to the point where he's worth multiple first round picks and how there will be so many teams after him. I don't believe there is any chance in hell that's the case given his age and injury history.
So he might get moved but the compensation isn't going to be as high as you think. I'll put it another way. I like Romo but if someone came to the Cowboys and offered say a 2nd round pick for him and then maybe a conditional pick that could turn into another 2nd rounder.......... I'd think long and hard about taking that deal.