One thing I have noticed as a grant reviewer is the variability in letters of support included for different proposals. Personally, I rarely look at them unless a critical piece of the proposal relies on the availability of that individual. In most cases, anyone who is critical to the proposal is involved with it, but there may be aim-specific methodology that leans on the expertise of another lab.
But one often sees many other letters as well. I haven't observed a direct connection to career stage and number of letters gathered, nor between prominence of the PI and letter number. When I posed the question of letter gathering on Twitter, the response was as vague. Some claim it is best to cover all bases, whereas others weren't sure how useful the letters were.
From my perspective, I can see letters being important in 3 situations: 1) When proposing to use some new methodology, 2) Proposing to use someone else's software/database/etc. that needs to be maintained, and 3) Ass covering for aspects of the proposal you do not have data for.
Do people really get letters from those they do not plan to work directly with to let reviewers know they are some sort of player in the filed? This is where things get murky for me. I rarely, if ever, see this in NSF applications. In fact, NSF recently forced all LoRs to be a single sentence basically affirming that the letter writer was down with whatever had been said they would do in the proposal. No more. I get the impression that letters are seen very differently in the NIH world.