I understand your argument, but you missed one major factor. Of the teams who have a need at DH, none will yield a first round pick. Let's take a serious look at the teams who may be interested.
Yankees, Angels, White Sox, Tigers, Twins-- not happening for reasons stated above.
Texas Rangers? Michael Young. Guardians? Hafner. Rays/Royals? I don't see them paying a quarter of their salary on a aging slugger, especially since they'll probably want to try to make smart moves locking up young guys early.
That leaves the Mariners, Orioles, Athletics, Blue Jays. These are teams at the bottom of the AL. Oakland and Seattle are pitcher's parks, and Seattle/Toronto/Baltimore have almost no chance of making the postseason in the next three years, so they will have to overbid to get him out of Boston.