At-will cantrips in 5e are a continuation of a popular aspect of 4e: everyone that has magic can always use magic, without having to rely on a crossbow when they're all "used up." I played my entire 3.5e career finding ways to have magic all day long, whether it was metamagic cheese (persistent spell, ftw), finding ways to wildshape into non-animal forms and get their abilities (aberration wildshape + Assume Supernatural Ability + Enhance Wildshape), or simply finding all-day spell effects. Having the system just let me make a magic-user at level 1 that gets magic all day without a bunch of books and esoteric optimizing tricks is a huge boon in 5e, IMO.
I remember sitting down at a Pathfinder game sometime after 4e was out. One of the complaints at the table about 4e was that different classes got spells that were too similar to each other. The wizard might get "Fireball," which was a AOE at a distance, while the sorcerer would get something like "Fireblast," which would be a fire AOE with a different rider effects. With this in mind, we started the PF campaign with a bunch of level 6 characters and, when the first fight broke out, 3 different characters, representing 3 different classes, were all casting the exact same buff spells and using the exact same tactics. So, in our 4e game, different classes had different powers that were similar and, in PF, different classes had powers that were literally identical. My problem with magic not feeling special in 5e relates directly to this.
You show up with a 5 man group at a fresh 5e game: Elven bow fighter, tielfing warlock, human wizard, dragonborn sorcerer, halfling cleric. The first time you enter a cave, you realize that most of your party can't see in the dark so ... all 5 characters cast the "light" cantrip. THAT is what stops magic from feeling "magical" in 5e, to me. My problem is that every character gets so, so, so much overlap in what they have access to off of the same list of options. I wish the sorcerer and wizard had different spell lists. I wish the wizard was broken up into around 3 or 4 unique classes with very little spell overlap. I'm tired of seeing parties where the wizard, sorcerer, specialty cleric, eldritch knight, and warlock all cast "fireball" in fights because everyone has casual access to the same stuff. The issue for me isn't how often you can cast a cantrip, its that literally everyone at the table can do the exact same stuff (likely, with the same DC!).