You probably also don't think, "Flying and invisible, while dropping meteors on people."
....which is why 5e felt it was cool if wizard couldn't do that. It's not key to the concept of "being a wizard."
A wizard in D&D has never been a great example of any classic fantasy archetype. A wizard in D&D is a wizard in D&D, and that's down to the edition to define what that means exactly.
For most people, they hear "wizard" and think "Gandalf" - and as the foremost paragon of fantasy wizardry, he wants to avoid using any sort of (useful) magic unless it's absolutely necessary. It shouldn't seem weird to get on board with that.
When thinking about game design, I find it's often useful to think about verbs. What did Gandalf
do that was different, that none of the other members of the Fellowship could do?
He used magic.
What do the students of Hogwarts do to fight their villain?
They use magic.
What did Merlin do that was exceptional among the Arthurian heroes?
He used magic.
When someone wants to play with that archetype, they often want to
use magic. That's what those characters do that's different.
Then the question comes up: okay, how often do you need to do that to feel like you're participating in the archetype?
Like, in terms of real-world time, how often? Every minute? Every five minutes? Once an hour? Once a session? Once a month? Once a year?
There's probably different thresholds for different genre expectations. How many spells per minute are in the LotR movie trilogy? The Harry Potter movies? How often (again, in real-world-time units) can wizards in WoW cast spells? What about wizards in a game like Pillars of Eternity? How many scenes with involve spells in the Harry Potter books or how many scenes with Gandalf involve them in the LotR books?
D&D is a game of imagination where a bunch of people sit around a table and talk in funny voices at each other and roll weird dice. How many times per hour do you need to pretend to cast a spell to forget that you're a dork at the dork table being dorky and imagine that you're a wizard in a magical land of dragons and knights? What if it's your first time playing D&D? How many minutes pass between your turns?
Would be 0% surprised if these metrics, in combination, lead to and encouraged at-will spellcasting.
That's just where the design ended up for the core books, though, and it doesn't limit what you can do with the game. "Doesn't have at-will spellcasting" isn't on my list of dealbreakers.
But...."DM thinks at-will spellcasting ruins D&D" is a ping of concern, if only because ideology driving your D&D game can be a recipe for disaster.