There are a few things at play here. IIRC, the $200/10yr offer was just prior to the arbitration ruling where Betts was granted $20M anyway. I'm inclined to call that the Red Sox opening salvo, but then he moves the goalpost significantly in both length and dollars when they approach his original demand.
Markets are not set in a vacuum. If they were, the BBWAA would be obligated going forward to induct anyone similar to Harold Baines because the Veteran's Committee screwed the pooch.
Re: WAR...For comparison purposes, Trout's WAR through 6 seasons was 47.5 and he was top 2 MVP vote getter in 5 of them, winning twice and one more after he signed for $35M per, up to 40 years old. a) What does this look like after Trout's age 34 or 36 season, assuming no PED's are in play? b) If Trout set Mookie's market and using WAR as a constant, the cross multiplication property puts Betts' AAV at $30.1M.
Finally, as an organization, the Red Sox already shot the moon (World Series victory) successfully, using Betts as a 9 or a 10, and are 26 points ahead. Other teams need him to be the Ace just to catch up.
Sports fandom (particularly professional) is irrational. Most root for laundry rather the human beings wearing it. I like Betts and he should get everything he is looking for. That said and as someone who understands that professional sports is not merely a game, I don't think any one organization in particular should be obligated to pay it to their (real or perceived) detriment.