I’m countering the claim that the scoreboard is any good for the game which currently has nothing but anecdotal evidence. The way I see it the burden of proof is on the people saying the scoreboard is necessary since, by default, there is no scoreboard unless it’s added.
Still, the evidence you’re asking for is easy to produce because it’s extremely well-established that social competitions arise from people’s inclination to compare themselves to others. Scores are an easy way to do that. You can read more here, here and here. It’s all about ego, and since comparing score this way hurts some people’s fragile egos or gives some shallow people an ego boost, all the encouragement a toxic player needs is right there at the end of a match on the scoreboard.
Surely you must’ve known better than to think this could be otherwise unless you’ve never competed with others in your life because this is something most people know from firsthand experience.