On a serious note, I'm starting to wonder if Belichick's salary cap philosophy is tied to red zone defense.
There may be a sliver of truth to this, but you pull in a lot of extraneous and even contradictory information to make your case. For instance:
the decision to break the bank for Gilmore over Butler comes to mind, as Butler is a less physical defender who can be boxed out in the endzone.
Given Bill's recent history with DBs, it is clear that height is not a required trait, nor is it anything that is built around at the expense of other factors. Height may had played a part in Gilmore's signing, but not in the sense you describe. Instead, it would be that Stephon checked all the necessary boxes.... and was also tall.
Then there are the facts that height isn't an EZ specific advantage and Gilmore "over" Butler is an inapt description of his acquisition.
Edge rushers are certainly less valuable as you get closer to defending your own goal line
This doesn't ring true at all. Pass rushing specialists might lose value, but a complete edge defender is no less valuable on the 5 than they are at the 50. It's not like teams can't run off tackle in the red zone. A case could also be made that quick pressure is even more important in the RZ than it is elsewhere.
whereas NTs and MLBs become much more valued.
If true, then NE would have made a more concerted effort to improve the ILBs in recent years. Instead, it's been HT and a bunch of developmental youngsters and league washouts. Granted, they've found some decent players, but the approach doesn't indicate a specific focus on the position. Even moreso when you consider that HT himself was no lock to be here this year (and his injury history).
Belichick didn't even try to resign Chandler Jones and traded away Jamie Collins.
It was pretty obvious after 2014 that Chandler didn't have a long Patriots life expectancy. He just wasn't well rounded enough to deserve the kind of contract his pass rushing skills alone would earn on the open market.
As for Collins, they only traded him away after making a lucrative offer and having him become a locker room distraction. Jamie doesn't support your thesis, he contradicts it.
I don't think Wilfork supports your thesis, either. Yes, he would be incredibly beneficial on the goal-line, but so is every NT in the league. What made Vince so remarkable - and, hence, worth a big investment - is his versatility. Not only was he terrific at the core duties, Wilfork was the rare NT who could play the edge if the match up required it. There is no reason to think a RZ bias had any influence on the decision to lock him up.
The question of why the disparity between yards and points is so consistent is an interesting one. Your attempt to explain it is admirable, but misses the mark, IMO.