Here are two claims:
(1) System makes no difference to the play experience.
(2) Many people prefer the 5e play experience to the 4e play experience, just as some prefer the 4e to the 5e play experience.
I don't think both claims can be true.
If one difference between 4e and 5e is the degree of ad hocery, and the role that the GM playes in that respect, then it makes sense that some people should focus on that as a cause of the difference in experience. And there's no reason to think that this is about "toxic GMing". Did everyone who didn't like 4e have toxic GMs?
System is ultimately unimportant in comparison to the people played with, but rules can get in the more or less, or be more or less elegant. The 5E rules allow for quick and elegant action resolution, without getting in the way.
The point about "toxic DMing" is that a DM a player needs to be protected from is not somebody that I would play with, or seek to work around with game rules.
Not all people. Some people. I'm also not sure what you mean by "a broader amount of play".
If the argument is that the popularity of5e is a sign of virtue either in the system or its players, I don't see how there can be grounds for complaint that those who prefer 4e want to point to the virtues in 4e as a system or in its players. Surely no one expects 4e players to infer that, because they are in a minority, they and their preference suck!
The popularity of 5E is a sign of fitness for most people's playstyle. What WotC found, in the aftermath of the reception of 4E when they did rigorous research on how most people play, they discovered that while the WotC insiders and a vocal contingent of Con goers, forumites, etc. had been playing 3.5 in a manner increasingly like 4E that made the changes seem organic, the vast majority of people playing 3.x had actually been playing 3.x like Moldvay/Mentzer Basic D&D with a bunch of suggestions in the books to use or not on an
ad hoc basis, as had been apparently the case with most AD&D play. So, 5E was built to fit the playstyle of the vast majority of folks, which is also why 5E burst Pathfinder's bubble, as the Crypto-Basic D&D crowd (the by-far majority playstyle, apparently) finally had rules that matched their play.
This isn't neccesarily any sort of virtue, other than commercial. But for those of us who had been playing this way the whole time, it is a breath of fresh air, and very freeing. I'm not saying it is by any means wrong to prefer the 4E style, but I do find the
ad hoc approach easier to improvise in play (which was the original point of the digression).