Hm. I don't have a problem with damage spells, in fact, given how many hit points monsters can have, I often find they probably could do more. The fact that damage synergizes with what the non-casters are typically doing is a big plus.
Hard control; things that leave enemies unable to do anything at all. These are problematic in every sense of the word. Hindering enemies actions and movements are exactly what I'd expect battlefield control to consist of in a game that wants melee combat to be the primary form of conflict resolution. Hypnotic Pattern making enemies stand around going "derrrh pretty lights" while you kill them one at a time seems a bit much. I prefer things like Web, Slow, or Sleet Storm.
I agree, summoning hordes is bad. A side effect of bounded accuracy is that more attacks are more useful than one strong attack in lots of situations. All summons should bring in a single, reasonable body that can suck up some hits, but never multiple bodies or spellcasting of it's own. I include Animate Objects here as well.
Out of combat spells. Things that grant a great deal of narrative power, especially on days where you're not adventuring (due to having depleted your Hit Dice on a previous day, or just downtime in general).
This gives casters a huge advantage on what they can do, and their ability to make money, gather information, and even stockpile resources without any real cost or risk can cause a lot of problems to a gamemaster who is not prepared for it. On the one hand, I like that these options exist, but on the other, they can be disruptive and make other players wonder why they don't have similar options.
Buff spells. I'm used to playing where a caster throws buffs on their fighters to make them more effective. But as a reaction to the 3.x era (I assume), buffs are conservative and often require concentration, directly competing with other, better spells casters can use. I would like to see this design space expanded upon; if the Wizard is using their godlike power to make the Fighter better, the disparity between classes can become far less of a factor. You just have to make sure they aren't buffing themselves, lol.