It is rare, and very valuable. I think you do one of two things--draft your QB, or trade down and fill multiple holes. I really would hate any other outcome.
The problem with trading down is that there are few positions in the NFL (I’d argue zero positions) where an impact player can make such a transformative difference to your team. If we assume they get 3-4 picks for #3, the chances of landing even one elite talent is slim let alone one guy whose value comes close to a franchise QB.
Filling those holes is important. But in the NFL nothing is as important as QB. Even pretty good/not mega star QBs are very difficult to find.
Even if you could guarantee the Pats could turn that 3rd pick into a very good LT (Trent Brown on his best days), a quality WR (think prime Deion Branch) and a solid defensive player (Pat Chung, Trey Flowers, Mike Vrabel etc), the value of all of that isn’t worth giving up the chance of landing a franchise QB. And the reality is you’re not going to hit on all the picks you get in a haul, it gives you more bites at a worse part of the apple.
The assumption in the “trade down and accumulate assets” mindset is that you’re going to land multiple key pieces. But the draft doesn’t work like that. You might get one high end player, one guy who is solid and one guy who flops.
There seems to be the thought “Daniels might suck” so go draft Alt/Nabors (etc) and get some picks in rounds where the hit rate (high end starter) is even lower. But you’re just spreading your risk without the reward of - if they hit - having the most important position in pro sports filled by a star.
Trading down and accumulating picks makes a lot of sense when the max value of what you’re potentially giving up is less than or similar to the max value of what you’re receiving (late 1st to mid 2nd tends to have similar upside players for example)
If you have a lottery ticket with a 25% of winning 10M are you trading it for a ticket with a 25% chance at winning 5M + 2 tickets with a 10% chance of winning 1M?
The value of a franchise QB dwarfs everything else in the NFL to the extent that any trade, assuming you have a QB need, makes no sense. It would have to be a wildly and unthinkably rich offer or they’d have to have an extremely negative view on all of the QB’s in the draft for them to be able to justify trading down.