This is an incredibly well formatted post. Very neat, well written, plenty of good questions and polls.
However, unfortunately, I say no.
Why?
Look at Stat shark. Stat shark, after entering the community, causes one thing and one thing only. Toxicity. People chose to discredit arguments simply because a player disagrees or has a worse player rating then them. Sometimes its fair; but also, their are plenty of times where it isn’t. This is I would argue already an issue on the forums, however we are lucky enough that the forums are well separated from the game and only a small portion of players choose to really engage with the forums.
Now, take this toxicity, multiply it by 20, and add it to every single player in the game. It is bound to go over incredibly poorly. It would drive me, and I am sure plenty of other players, far away from the game.
TL:DR; The use of statshark on the forums shows that if SBMM entered the game, toxicity and poor sportsmanship (or whatever you want to call it) would be rampant and it would ruin the game as we know it.
TLDR…at any rate matching should first look at time played. a 100 hour player vs a 10k hour player in no way makes any sense. One has brand new crews, doesnt know maps or where to shoot while the other is maxed across the board and simply is farming KD. All this does is scare people away.
Stats have destroyed every single game its ever been put into. Take World of Warcraft, different genre but same thing occurred. Gear score apps came in and now you had this new filter to gauge people against. Got so bad Blizzard forced the removal of the stats it used.
Destiny 2…Raid Report and Trials Report ruined it as well. Now you are gauged off numbers you may or may not have had any ability to control.
Only stats should be allowed are the ones currently in game. Remember also whoever makes that website is financially benefitting off adds using your data.
one idea that could make your suggestion relevant would be to implement the bungie era halo skill based matchmaking (the best one ever), one game you face stronger opponents, the other weaker opponents, etc.
Also the SBMM should be balanced by only giving you stronger players to fight when top tier, and weaker when low tier, the other way around is just not possible.