As I stated in the OP, this is primarily about PC casters.
I hope you read all this!
I think the Bard, Cleric, Druid, Warlock, are all perfect where they're at in terms of capabilities.
Bards have a good support and condition list with little damage involved. Very much trickster magic.
Clerics have the most healing, as well as a number of support spells.
Druids have a lot of conjuration, emanation, and nature-themed spells.
Warlocks are primarily blasters and cursers that have a dark fantasy aesthetic.
That leaves Sorcerers and Wizards as issues for two drastically different reasons.
Sorcerers have a strong Arcane list now but the spells in it are a bit too rigid. Sorcerers could do with a revamp, where they get most of their spells from their Subclass, and their base spell list include spells that can flex to fit theme, like how Chaos Bolt can have different damage types etc.
Wizard is an abomination that has every literal super power you could ever imagine on its spell list. I truly think it is a huge weakness in D&D design to have the wizard class as is. It sucks up so much space both thematically and mechanically. It's the "choose your own mechanics" class where you can pick and learn every spell to change your build as you want. So big is the spell list that it makes it hard to add new casters, because so many genres and themes of magic are ate up by the wizard. They can do all eight schools in high amount.
On a more specific level, some spells are IMO too low of a level. Charm Person, Hold Person, Bless, and Guidance are IMO too accessible. 3rd-5th level spells are altogether fine.
6th-9th level spells are also fine, but I think that 9th level spells should have a longer "cooldown" on them. Being able to grant a wish every day is IMO the domain of deific characters and archfey etc. Being able to grant a wish every week and risking losing it is much more mortal IMO.
6th, 7th, and 8th level spells don't generally have effects all that crazy. Disintergrate is cool, so is FInger of Death. But the flashy spells like Earthquake or Tsunami have really small areas of effects. These spells FEEL like 3rd-5th level spells but with bigger numbers.
There are standouts, of course. Forcecage. Plane Shift. Teleport. Forcecage is an issue of mechanical balance, but the other two are often complained about because of what they allow. But Teleport is essentially just fast travel to a place you've already been; it's real function isn't to kill exploration challenges, but to drastically increase the pace of the game. This is reinforced by how teleport is dangerous to use to places you've never been before.
Plane Shift probably shouldn't be a spell IMO. I think it works better as a magic item. Regardless, Plane Shift essentially is the "license to expand your campaign into more esoteric lands" spell. In other words, its a spell of
aesthetics, that is, a spell meant to add new flavors to the game. Ultimately, I don't think it disrupts play, it just forces the GM to think more fantastical.
I think one potential problem I haven't discussed yet is the amount of spells each player gets. 5R essentially increased the number of spells every spellcaster now has access too. I'm not sure if I agree with that. On his patreon, Mearls has started introducing spells in 5 tiers, and each spell has a "Beyond the Rules" paragraph at the end of its description. These paragraphs tell the GM other acceptable and creative ways the spell could be used. An example is Spiritual Weapon could recreate a legendary weapon or relic, which could effect religion checks or audiences with NPCs and so on. A spell like Bless could be used to just give someone a good day if no die is rolled for the bonus d4. Etc etc.
By decreasing the number of spells, and by encouraging DMs and players to use spells creatively, you create much more sensible caster PCs. Right now, caster PCs ultimately feel
unwieldy. You start with a handful of spells but once you have more than 8-10 of them + cantrips + class abilities + magic items + feats, it gets hard to keep up with. Each spell is essentially a feature that you have X uses of per short or long rest, so as compared to a Rogue, a spellcaster has 10+ more features. You have to think about how to sue these features, when they are most effective, what they do, and so on. It's just a lot. But when spells can be used in more creative ways, you cut down on what has essentially become spell bloat.
I think also think some spells could be given more significant benefits when cast at higher levels. For example, Fireball. If Burning Hands is level 1, maybe casting it as a level 3 spell makes it into Fireball, and Level 7 makes it into Firestorm. This means fewer spells, and that the spells you do choose are more impactful not only because of Beyond the Rules stuff but because the spells change as you grow more powerful.
But to get back to your original question, I don't think most spellcasters are doing too much. I think they are just overburdened by too-similar options, and that Wizard sucks up way too much space.