Honestly I agree with your hot take, if 4e had come out in the opposite order, starting with the essentials stuff, and then diversifying into the PHB style, it would have helped it a lot-- probably not scared off the 3.5 fans in the first place. Give it the quality of digital tools we see today (if it was taking the place of 5e), I think people would really prefer it for both its hands off approach to out of combat roleplaying, and its more engaging game play. Honestly, given a few more years, I think digital tool use is going to be so ubiquitous its going to start radically changing the narrative on accessibility vs. engaging game play in RPGs, because people will be more comfortable letting their tools take the burden of actually book keeping, and just enjoy the depth on offer, my players already do this and it works super well. I think its already been accelerated by the COVID shift to virtual tabletops.
My personal opinion is that pf2e actually fulfills that niche even better though, since its a lot more approachable than either 5e or 4e or pf1e in terms of how much character optimization it takes to succeed and how wide the party gap can get, it just doesn't benefit from the Coca-Cola like status of Dungeons and Dragons as a brand.