So cut a bunch of guys who made too much last year then throw all that money at long term extensions for a bunch of guys who aren't even entering free agency. This kind of cap strategy is what lands teams in cap hell, and the Pats' refusal to operate in this way is a huge part of why they've been Super Bowl contenders for the better part of two straight decades.
That said, I don't really disagree with most of this, at least in the broad strokes of it. Picking up Brown's option is basically a no-brainer considering what else the Pats have as alternatives. I agree that signing him to a long-term deal is pretty much a coin flip at this point; he's an asset, and worth keeping around long term at the right price, but he's not the kind of instrumental guy that you make your top priority or place much of a premium on. Extending Mason and Flowers is ideal: both are young, key players who are very good at what they do, have flown under the radar a bit so far, and might be signable at a reasonable price. I dunno if it's realistic to extend everyone this offseason, but Mason and Flowers are exactly the kind of guys you want to keep around long term even if you have to pay a bit more than you'd ideally like to pay.
But I'm really not sure re: Cooks. He's a very good WR, but I wouldn't give him top-10 receiver money; that kind of cash is better spent elsewhere IMO. He's not a guy who dramatically changes the complexion of the game just by being on the field, in the way that the absolute top tier guys do, and as a general rule I hate the idea of paying top tier money for guys who don't meet that standard. Then again, I probably wouldn't have traded a first rounder for Cooks in the first place, so I think it's pretty clear my understanding of his value is not in line with Belichick's.