I said attack rolls should be primarily about dealing damage, and major status effects should grant a save. Nothing in there says you can't have saving throws against damage.The spell creation section of the DMG, for example, doesn't say it's inappropriate to have a non-damage effect tied to an attack roll - and the game has more than one example of things which, according to your stated principle, should be attack rolls but are actually saving throws. Even the classic area damage spells fall into what you say attack rolls should primarily be about.
How many effects are there that impose a major status effect with neither a save nor a hit point threshold? Offhand, the only one that comes to mind is contagion - which has also been widely criticized for the exact same reason.
A 9th-level PC can hit Demogorgon on 13+ using just a regular attack roll. And there are lots of ways to pile bonuses on attacks. A d8 from Bardic Inspiration, a d4 from bless, and advantage from one of the myriad ways to get advantage, and that same 9th-level PC is hitting the Prince of Demons better than nine times out of ten.As for getting legendary resistance but not legendary dodge, that's not completely accurate - most monsters with legendary saves have high AC, and a high enough AC has a similar effect to legendary saves.
Legendary Resistance provides a safeguard against bonus-stacking shenanigans. It's much harder to penalize enemy saving throws than it is to boost your own attacks, but even if you find a way to do it, Demogorgon gets three chances a day to say, "Nope. Try again." Attack rolls don't normally require such a safeguard because even if you hit with every attack, you still have to chew through hundreds and hundreds of hit points. Effects that paralyze on a hit with no save are a major loophole.