This is an interesting question. There's been some studies showing that if a player believes that 'strategy' is necessary to overcome a challenge, he will keep trying after he fails because he believes 'strategy' is something that can be improved upon.
However, if a player believes that 'physical attributes' like speed or actions-per-minute are necessary to overcome a challenge, the player is more likely to quit after the first few failed attempts because 'physical' speed is something that is difficult to improve.
This study doesn't directly map on to your example, but the similarities are interesting to consider. Ultimately, I'd love to be able to design features that reduce the triggers that cause players to go toxic after a negative outcome.
Even for support mains, support can often feel like a wasted role b/c there is only so much you can do... Do you think the live team and champion design team could benefit from a psychological study and analysis of what makes a champ "rewarding" to play when they basically deal zero damage?
You cite that ppl often feel they can re-try if "strategy" was the problem, but not if "numbers" are. Often when I play support and give up in a game, it's because I know that I cannot produce the numbers to win... Even when I pull my cc's well, peel well, but just can't actually do anything damage wise, well eventually they're no longer stunned, slowed, w/e and are still at full health :\
I play support a lot, but really feel like too often strategy isn't the problem... Being unable to make a difference even when playing well is :\