Ruin Explorer
Legend
By level 20, they effectively have advantage on all saves three times. Given that all of the old save-or-die spells I've seen have a save every round now, that will help enforce a maximum duration for any mind control spell.
That's a different thread, but no - Fighters can expect to have between 5 and 35% chance to make a WIS save at that level, assuming enemy caster stat cap of 20. Even at 35%, which assumes a FTR with 20 WIS (!!!), Advantage means you still are quite likely to fail (30%, I believe). With a more likely 14 WIS, and thus only a 20% chance, you probably still fail, even with Advantage. WIS 10 has only a 10% chance.
Note that all the "better" CC spells do NOT do what you describe. Dominate Person is save at start, no others (have to hope friends break caster's Concentration, whilst you hit them in the face), for example.