What makes this kind of mentality all the more nonsensical is that kill rewards are only handed out to whoever lands the last hit on a champion: you could very well have done most of the work through damage, CC, utility, etc., but unless you land that very last bit of damage on your target, you're slated for an assist and nothing else. It's a terrible mentality that cuts both ways: for classes that aren't focused on damage, like supports and tanks, it feels like they're relegated to eternal sidekicks in a game that puts the spotlight exclusively on damage, with both gold and credit, but to those same damage classes, especially the marksman, it makes them feel bad for not getting the last hit in a fight they contributed to, and even when they're doing well, it often leads to the accusation of them being spoon-fed champion last hits.
On top of this, the whole artificial kill/assist separation leads to these awkward dances around enemies at low health to avoid "stealing" the carry's gold income with an accidental autoattack or the like, and when targets inevitably get killed in chaotic fights by the "wrong" player, KS accusations can be so emotionally charged that they can sour the mood and impede play through pointless arguments, sometimes even ruining games completely if players get too spiteful. Effectively, the separation between kills and assists is so thin in practice, yet causes so much distress and misinformation when put up against fast-paced gameplay it can't handle, that it is almost purely detrimental to the game as is.
I think the alternative to this, which would also solve the issue mentioned in the OP, is to basically just remove the separation between kills and assists and bunch them together under takedowns: pretty much every kill-based reward in the game has been changed over time to apply to assists as well, precisely because it avoids players having their day ruined by an ally who may have otherwise had good intentions, or just wasn't paying attention. Since takedowns would represent how many kills you participated in, regardless of whether or not you landed the last hit, it would be a much more accurate measure of each player's kill contribution, and would allow non-carries, particularly supports and tanks, to truly shine without needing more damage. Since the number of takedowns any player performs generally exceeds their number of personal deaths, it would also muddy the kind of asinine accusations salty players would try to make when putting their teammates down for their scores -- even if a team is doing really badly, having a takedown/death ratio of, say, 10 / 8 wouldn't look nearly as bad as a KDA of 3 / 8 / 7 , despite being essentially the same score.