Is it possible that magic seems less special in 5th edition because many of us here have been playing D&D for years? Spells like Fireball should be wondrous and terrifying, but after 5, 10, or 30 years seeing it in games, well, it kind of loses its impact.
I don't feel like that's the case for me, and I've been playing for 40+ years. For me, magic seems less special because in 5e everyone can cast some type of spell - between class/subclass/feat/race/background, etc. Everyone has magic, unless you decide specifically not to (i.e. Champion, and even then, they could Feat into it, or get a cantrip by being an elf, albeit, likely suboptimally).
In Ad&d, a Wizard could cast Fireball at 5th level, but only after getting 20,000xp and surviving with d4 Hit Dice (usually in a party of 5+), AND finding a fireball out in the wild (which usually means getting it dropped on you first).
In 5e, that same Wizard gets to 5th level after 6,500xp with d6 HD (usually in a party maxing 4 players), and PICKS 2 spells each level, so is guaranteed to get what they want.
That Ad&d Wizard has a total of 7 spells to cast, pre-memorized, no swapping out. That's it.
That 5e Wizard has 9 Leveled spells to cast, plus 4 Cantrips at will, that never run out, and can and Arcane Recovery to get a few back. And can prepare however many spells and use the ones that are most helpful. Then add in rituals, etc., and the capabilities go on up.
Just the wizard itself has become easier, more flexible, and IME, doesn't need to rely on party members as heavily as older games. That, plus the fact that anyone can cast spells or spell like abilities if they want to makes it feel like the odd game is the one with little to no magic, and every game is
expected to have everyone throwing around spells. THAT gets boring to me (and this from someone who likes playing Wizards).
If Wizards had to roll "to hit" like every other class with all of their spells (or call it a casting roll, whatever), and then remove saves, I'd be better inclined. But as it stands, as has been mentioned, there is no danger to spells, very little chance to miss unless you're pew pewing cantrips all day, and aside from saves, which halve/remove damage and effects, that's the limiter.
Also, the fact there are 215 Wizard Spells alone in the PHB speaks volumes.