Sure. But I guess the question is, how much more?
A fair bit. If you want numbers (in whatever abstract, analogic sense these numbers apply), I'm talking solid plurality to slim majority. 45% to 55%, with no other individual factor being as impactful.
People hating on grappling rules in most editions, for example, or the solid majority opinion that descending AC was unwise and THAC0 was outright bad, or the whole XP=GP thing shaping player psychology etc. Many of the ways edition matters are in the style of that third thing, e.g. the way 3e handled magic and buffs meant supportive teamwork was actually really inferior to just doing things yourself and thus cooperation was significantly
discouraged despite that actually being the opposite of the design intent.
Is it enough to make a big fuss out of it?
Depends. Are you casting aspersions and treating "a big fuss" as people throwing a tantrum simply because you disagree with their motives? Or are you saying people are taking a legitimate issue and blowing it somewhat out of proportion? Because your words read as strongly leaning toward the former, and if so, I vehemently disagree with that. I
do think it is worth at least a decent portion of the attention it gets, and I find a lot of people have very flippant, dismissive attitudes about legitimate concerns.
Is it enough to argue that systems are so important that genres need to be relegated to specific systems to be considered worthwhile for that genre?
Has anyone done that? I haven't. My concerns barely touch on thematic expression. Most thematic content is comparatively orthogonal to the mechanical content anyway. I'm a big fan of reskinning, and have seen it work well e.g. my favorite 4e game ever was a science-fantasy cyberpunk-ish game with "grim but hopeful" space opera vibes. It required the addition of literally just two skills (essentially "tech" and "xenobiology")
Has the importance of system been exaggerated by people who enjoy creating systems or people who enjoy discussing systems because of that enjoyment rather than because systems are really that important?
No? I don't enjoy creating systems. I very much prefer to leave the hard work of system design to other people. Because
actual system design, where the designer understands that this is a
technology as well as an expressive medium, where you do real serious analysis of your work (using statistics, effective
and unbiased survey design, and collecting a large enough data set to actually derive meaningful results), is very difficult and requires a lot more resources than those available to a lone dude plunking away at his keyboard for a couple weeks (or whatever.)