I could see the award going either way, but I see a few reasons Allen won it.
-It's not an apples to apples comparison, but Lamar won it last year with not the strongest MVP year. His statistics were not that of your recent MVP winners. Obviously, this year is a bit different as Lamars numbers were incredible, but it opened up for the door for some voters to go with the, "Well, last year I voted for Lamar due to lack of weapons and talent, so I'm voting Allen this year". Not saying it's right ,but that's definitely what happened with some voters.
-It shouldn't impact voting, but there are definitely those that would rather see someone win their first MVP instead of their third.
-I'm sure people let his performances or perceived poor playoff performances influence their decisions.
-I honestly don't think Lamar has all of these "amazing" weapons in Flowers, Bateman, Andrews, Likley, etc, but adding Henry was clearly used against him or in a case to argue that Josh Allen had less to work with. For me, it's the same argument people would make about Purdy last year with him having Cmac. Granted, seasons are not apples to apples and their are differences, especially with the level Lamar played at this year, but that's obviously a big part of some voters decisions.
-I'm actually not shocked at the first-team all-pro vote for Lamar and the MVP for Allen, although I do find it somewhat idiotic. The argument is likely that Lamar had the "better" and more impressive season, but Allen was more "valuable". It is also an easier out for those that weren't going to vote for Lamar for MVP, but gave him the first-team all-pro selection instead.