Because I can't point to an actual reason other than wish-casting that he'd actually pick the Red Sox (and I think even the scenarios I painted to make an argument, which are the Sox history with Japanese pitchers and YY, I don't think either of these will come close to out weighing any of the below).
1 - If it comes down to decision of nothing but money, (ie it's truly an open bid situation, where the agent always goes out to other teams with whatever the highest offer is at the moment and asks if they want to beat it until everyone else says no), I don't think Steve Cohen will literally ever stop bidding up. Mostly because of the kazillionaire owners in one Yamamoto, he's probably the most desperate (and should be). The Sox won in 2018, the Yankees in 2009, the Giants whatever year they last won - maybe 2012. I don't count the Dodgers title in 2020, and I don't know if they do. If they see 2020 as the sham most on this board do (self included) they also join the Mets at the top of the desperation list.
I don't think this means he's certainly a Met, other factors than money could come into play and at some point probably will ( when it won't affect you, any generation of your family for 200 years or any charity you'd ever want to donate to, is there really that much of a difference between 10/$325m from NYY and 10/$335m from NYM...?). But if it really is just about the highest offer, I would picture Cohen being the last to blink.
2 - If deals are relatively "equal", I assume he chooses the place most likely to win the most while he's there. The way the teams are set up for the next call it 3 to 4 seasons, the Sox (and Giants and Mets) are a lot behind LAD and NYY at the MLB level. The Sox are also pretty far down the list in terms of what that looks like in the upper minors even if Fangraphs loves (and even if they're right) about what Bleis might become in 2027, especially if someone thinks that starting pitching is important in baseball.
3 - If deals are equal and he's not concerned about likelihood of winning titles in the next 3/4 seasons, I assume he'd pick somewhere relatively closer to Japan with a larger Japanese population (meaning LAD or SF anyway, assuming this data from Wikipedia can be counted as reliable
https://en.wikipedia.org/wiki/List_of_U.S._cities_with_large_Japanese-American_populations). Granted, you're talking about roughly 3 hours flight difference and it's not like Yamamoto is going to be deciding if he should spend the extra $300 to get slightly more leg room on Jet Blue, but again if literally everything else is equal, I think one would pick the larger Japanese community with 3 fewer hours on a plane.
4 - I chose to isolate 3/4 seasons because who knows what the baseball landscape will look like in 5 years. I mean, I know that for certain after the 2018 season when the Red Sox had a cost controlled core of Betts, Benintendi, Bogaerts, JDM, Devers as a rookie, Bradley Jr, Price, Sale, Porcello and Eovaldi with Casas, Groome and Houck and had just obliterated the Yankees, Houston and LAD in the playoffs, I didn't assume that by 2022 they'd be irrelevant in Boston and pretty much irrelevant in baseball.
I don't pretend to know what motivates Yamamoto, but if he's anything like most professional athletes either money, winning or comfort are probably higher on the list than "wow did that town embrace Koji a decade ago" and the Red Sox don't come out 1st (or even 2nd) in any of those categories. The only chance I think the Sox have is that YY really does consider Yoshida one of his 10 best friends in the world and doesn't consider someone on one of those other teams similarly - and I don't believe anyone has even intimated they're THAT close.