I have complicated feelings about blaming these two specifically.
On one hand - are they, and their respective stories, the origin point for all the shittiest isekai stories? Yes, absolutely. Mushoku Tensei's adaptation is recent, but it should be stressed that the source material dates back to around the same time as SAO, and the amount of stories that draw from it is staggering. Of course, most of those stories suck ass.
The thing is...Mushoku Tensei doesn't suck. Wait, wait hang on, let me explain! I'm not going to say the story isn't deeply, deeply problematic - because it is. It absolutely is. However, that doesn't preclude it from being well written. Mushoku Tensei, for all it's many fucked up elements, also does a lot of things really really right as a story. That's why it's so controversial - if it just sucked people could ignore it.
Mushoku Tensei is a story with strong and detailed worldbuilding, and is absolutely fantastic at making that world feel real, and lived in, and like it exists outside of it's main protagonist. It's cast is absolutely packed with varied, compelling, compellingly flawed, and fully fleshed-out characters who have equally compelling character arcs where they struggle with those flaws and grow as people in belivable ways. Even Rudeus, for all his scumbag personality traits, is written as a complicated, multifaceted person who (and this is not me excusing his actions or the way the story tries to excuse them) legitimately grows as a person throughout the story. It's a story that's willing to take the time to show every step of the journey, to commit to telling the full story of it's protagonists life without rushing to the cool and epic parts because it believes that the things he learns in the slow parts are just as important. It actually commits to the entire premise of Isekai - the idea of the second chance, and builds it's entire narrative around that theme of second chances. It's a story with things to say, an actual artistic point to make, and everything in the story works in concert in service of those themes.
What I'm trying to get at here, is that everything that Frieren does right (and Frieren does fucking everything right, that series is a masterpiece of masterpieces), Mushoku ALSO does right, and in some cases better. And I do mean Frieren specifically - there is a LOT of overlap in the overall tone of the two stories and their approach to storytelling. It's just that Mushoku also does a lot of things wrong on top of that, particularly as it relates to it's protagonist being a perverted piece of human refuse.
The issue is that becuase of aforementioned Legitimately Good Writing, Mushoku got popular. Because it got popular, it got imitators. Those imitators aped the surface aesthetic of Mushoku, copied all it's problematic elements uncritically, and stripped out everything good because those shitty problematic elements pander to the lowest common denominator of shut-in pervert losers who just want trashy wish-fulfilment power fantasies, wheras letting your protagonist be more than a blank-slate self insert and having female characters have realistic flaws and actual personalities doesn't.
As for SAO, well SAO was never a masterpiece, but it's really worth noting that it's only bad by the standards of it's time. SAO may not be amazingly well written, but it wasn't the same story over and over again with a slight riff. It attempts to be original, it attempts to play with unique ideas, it attempts to go legitimately creative places with the story. Even Kirito, bland ass motherfucker that he is, looks a lot better when you consider that no, he wasn't created as a lazy riff on Every Generic Anime Protag Ever, since most of those in modern times are riffing on him.
Is SAO good? Fuck no. But it's also not unoriginal, or lazy. It's writing lacks competence, not creativity. It does not have good character writing, or a good main plot, or worldbuilding that makes sense, or any understanding of what an actually good vrmmo would look like. But it had a lot of plot beats that were legitimately unique for it's time, and a lot of plot beats that still ring as unique now, and the fact that it dares to be incompetently creative, as opposed to incompetently derivative, makes it still stand head and shoulders above it's knockoffs.
So while both series are the origin points for basically all the worst modern trends in anime...it's unfair to not point out that they are also nearly universally better than all the series that copy them, barring occasional exceptions.
If you want to see the fantasy of SAO played straight, written by someone who actually understands what makes a video game fun and is confident enough in their writing to not even need a death game gimmick to keep the story compelling, watch Shangri-La Frontier.
If you want to see Mushoku Tensei minus all the shit parts of Mushoku Tensei, while keeping all the great parts of Mushoku Tensei, watch Frieren.
If you want to see a brutal deconstruction of shitty power fantasy isekai in general, and an extremely pointed callout post towards all the losers who are like pre-isekai Rudy, project themselves onto Kirito and all his knockoffs to feel better about their terrible lives, and feel entitled to all the respect (and women) that both characters get without being willing to accept that they need to fundamentally change their terrible personality and mindset to make that even a remote possibility, watch Re:Zero.