Having played casters, it might be "prima facie obvious", but as I think we all know prima facie knowledge is not a fact. Whenever I've played casters in 5e, I've struggled with the limitations imposed by both prepared/known spells and with spell slots. Perhaps I'm just bad at playing casters, but I don't think that's the case. In at least some of those cases, I was in a party with other casters. Monsters making saves when I was sure they would fail was yet another issue.
I really feel that those who believe casters are some much more powerful are looking at only ideal circumstances. They always have the right spells prepared. They never run out of spells. Monsters never make their save or have counters for spell effects. Circumstances are always in the party's favor. The casters can survive long enough to become high level in the first place. So on and so forth.
I mean, sure, the summon spells are potent. But, except for certain druid spells, they take a minute to cast and only last an hour. Additionally, if you lose concentration the results could be somewhat disasterous. Planar binding can extend the duration, but it had an expensive component so you won't be using it regularly until high levels.
From your attempt to describe spellcaster strengths here, I think what's going on is that you
are "bad" at playing spellcasters. You're superficially correct in your criticisms of a certain caricature of spellcasters, but the very criticism reveals a simplistic first-order view of how you think spellcasters ought to be played: reactively, haphazardly, relying on luck, with an eggshell perimeter defense instead of defense in depth. Even the way you describe losing control of an elemental is revealing. If you're putting yourself in a position where losing control of an elemental is disastrous, let alone
likely and disastrous, you must be courting disaster already. (It's like those people who claim that an inconvenient critical hit is disastrous for them--if it is, either you're playing extremely challenging scenarios already or you're doing it wrong.)
Yes, spells known and spells prepared are very real constraints, and so is concentration. That is
precisely where my observation about multi-wizard parties comes from: some of the best combos and synergies come from removing those constraints. I already mentioned the brokenly-good Wall of Force + Cloudkill combo, and it should be obvious that having 3x as many wizards in the party goes a fair way towards removing that "you won't always have the right spell known + prepared" constraint you yourself mentioned. I could name a few other multi-concentration combos (Haste + Polymorph into T-Rex is amazingly fun and effective, especially if you exploit the mobility aspects; and it works just as well on a wizard as it does on a fighter unless you have an unusual interpretation of Polymorph) but the deeper point is simply that: spellcasters have more affordances, and in particular more
proactive affordances; and non-spellcasting affordances in 5E are front-loaded. Yes, Rogues are great; but a Rogue 2/anything 18 is approximately as amazing as a Rogue 20, so you can afford to fill up the rest of your levels with something that gives you more affordances, like Rogue 2/Bladesinger 18. And now you're a Rogue who can use his invisible familiar to scout ahead while he follows invisibly behind, and can Teleport to safety if he needs to.
I don't want to derail this thread much more, but the criticisms you make ("you don't always have the right spells prepared") reveal a reactive mindset that to my eye explains why you've struggled with spellcasters. And I agree with your criticisms to an extent--many people who like to moan about "caster supremacy" are just wrong, and they're wrong in exactly the ways you identified. A wizard
doesn't have unlimited spell slots, and you
can't judge merely by peak performance in ideal situations. But the next step is to look at the actual proposed party (e.g. necromancer, summoner, two bladesingers if I recall correctly which thread we're in) and consider what is the number and variety of situations in which the party is prepared to excel. If you choose your spells wisely, that number will be very high.
As an aside: Rope Trick should be a mandatory spell for any party which includes members (bladesingers, moon druids, warlocks) who have important abilities that recharge on a short rest.