Given that third-party Android OSes are missing features that many people consider essential (like anything that requires passing SafetyNet), I don't believe these OSes are a general solution, applicable to the masses, even if installation were dead-simple and reliable.
I ran CyanogenMod for years, and every app I ran and every feature I used on the stock Android OS worked properly on CM. I loved it. But these days that's just not the case on Lineage or Graphene or Calyx or any of the others.
So I think for many people, it doesn't matter. "Google Android", "Samsung Android", etc. are the only realistic options, so they are just "Android" to them.
"Pushing back" doesn't really work when there's no support, and adding that support is against Google's priorities.
Regardless web experience on mobile is unfortunately generally subpar than native apps, for most sites/apps. I'm not sure I'm equipped to change that situation.
I ran CyanogenMod for years, and every app I ran and every feature I used on the stock Android OS worked properly on CM. I loved it. But these days that's just not the case on Lineage or Graphene or Calyx or any of the others.
So I think for many people, it doesn't matter. "Google Android", "Samsung Android", etc. are the only realistic options, so they are just "Android" to them.