It's the same concerns I shared when they landed Teixeira. Getting a young superstart, a top 5 player at his position, is never good for the Sox if the Yankees land that particular player. Your analysis is pretty much spot on.
This is a very salient point and one that I think gets missed quite a bit...in 4-6 years, when ARod and Tex are nearing the end of their deals, they will need to keep that DH spot vacant for them.
I don't think it would stop them from comitting long-term to Holliday, though.
I don't think signing Bay makes them stupid. I just think they wouldn't be as good as they would be had they signed Holliday.
I can't judge the worth without seeing any kind of contract number though....but if you ask me, I think Bay signs for Drew money while Holliday signs for Tex money.