I did a bit more research and found this is far, far, FAR from the whole story. For example, in 3.5e, the dominance of spellcasters had a lot to do with their ability to buff themselves sky-high, which is gone from 5e thanks to the concentration mechanic and reworking of buffs, killing CoDzilla. Also, spells no longer gain power automatically (outside cantrips) and non-spellcasters received significant buffs that make them more dangerous and survivable, such as barbarian rate halving damage received and rogues getting unlimited 3e style defensive rolls with no save needed at level five. That last one will be interesting to see implemented, actually.
Charm and illusion spells will still mess up your fighters on higher levels. Magic was never really about dealing damage, it was about control, and casters still have that covered.