I was running a M&M game set in 1914 for experienced gamers a while ago. One of the guys wanted to make a super-speedster who could do the very genre-appropriate rapid-fire punch. The systemic design against having iterative attacks made the methods available to design such an attack very unsatisfactory.
I have to agree with this train of thought.
It seems to come down to genre and genre emulation more than the system itself in most cases. The system might not matter in a vacuum, but the system's ability to emulate the genre the game takes is incredibly important. A system that works for a given genre will make a better game. If the fiction of the game doesn't flow, then its like watching a movie where the special effects are incredibly transparent - without the ability for that to be so bad that its funny.
As an extension, once you've played a few games that are really good at their genre, other games that aren't start to look clunky or not as appealing. As an example, if somebody wants to play a noir murder mystery, I'm going to be comparing the system to GUMSHOE in my head and it better stand up. If it doesn't, it just won't feel right.
And, then, of course some people just don't like some genres. A friend of mine doesn't like Star Trek, so no Star Trek games for us. It doesn't matter how well the system plays out a "great" game; he'll not enjoy it because he just doesn't like Star Trek.
Yet, is your fun at the end of the session diminished in a significant way because d20 modern was chosen over Gumshoe? How much does it actually matter?
I was running a M&M game set in 1914 for experienced gamers a while ago. One of the guys wanted to make a super-speedster who could do the very genre-appropriate rapid-fire punch. The systemic design against having iterative attacks made the methods available to design such an attack very unsatisfactory.
In an otherwise good system, that glaring oddity seriously impacted his enjoyment...and that of others.
I think it's a myth to state that a game's system dictate's how well a game will run.
How much does system matter for the players to enjoy themselves?
I think the analogy is flawed because ultimately you are talking about how people interact with each other, rather than the mechanics of a machine.A good GM has the potential to override a bad system, just like a bad GM can override a good one. But generally speaking, its still better for all to start with a good foundational system regardless of the GM's skills.
With the equalizer on a sound system, you can control bass and treble independently- some even beak down your sound into a large number of independently controllable ranges.
Similarly, system quality and GM skill (and other factors) vary independently to create your gaming experience.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.