You're right. It's only base dice, no modifiers.
This probably sounds terrible, however, there is a good reason:
It's more balanced than it seems.
It's hard to tell sometimes; believe me I know. But, until you get more hands-on experience with the game, you have to give the game you're playing a "grace period" where you trust that the designers made the correct decisions, even if it seems like they didn't at first. Every campaign you play or DM is going to be different. If you change players or DM, then the campaign will be completely different. Some of those games, you will have players that built weak casters, and experienced grognards that built martial types. Although it is a roleplaying game, the "player skill" of the game comes in with decision-making during game time, and character building during creation.
That said, if you GM a game and you consistently encounter the same balance issues across encounters, then yeah, you should feel confident that houseruling whatever the issue is will improve your experience.
Your Wizard's spell slots are pretty big.
Bear with me a moment and imagine that the Wizard class is actually Batman. The biggest strength of the Wizard is that they have a tool ready for every situation -- at least, if they're a good Wizard. That's the player-skill-decision-making part. The spells your Wizard picked aren't bad, they just make him very good at things that aren't combat. Your Wizard has a ton of tools for dealing with non-combat situations. Imagine if Batman didn't bring his Batarangs when he went out on a mission. He's still the best detective on the planet, but now he isn't as effective as he would be in a fight. Spells are really, really good at solving specific problems.
That said, given the nature of the encounters you described, you might try throwing your Wizard a bone if you haven't already. D&D is more than just combat, and if you aren't giving your non-combat specialist Wizard any non-combat to specialize in, he'll feel like a useless player. If your player is concerned about his build, then you can allow him to switch out a cantrip, or give him a couple of good AOE scrolls in the next loot pile to scribe.
In addition, cantrips scale at certain levels. It's not immediately, but you can be sure that the cantrip will be a good standby at later levels.
You do have a good point here: if the group encounters a pit trap (or, as you say, a broken bridge, a well, or a chasm), and there isn't anything complicating the situation, then a flying character can just carry the group past that.
One counterpoint would be that most of these hazards probably weren't that interesting in the first place, because "grappling hook and 50 feet of rope" is standard adventuring gear, and that also lets a group bypass a pit trap / broken bridge / well / chasm.
But I think there are two deeper issues here.
One is that the function of challenges is not actually to make the players' lives difficult. The function of challenges is to let the characters show off how awesome they are by overcoming the challenges. If you narrate a sixty-foot-wide chasm, with a hundred-foot drop to sharp rocks and a raging river, and then the aaracokra says "okay, guys, I carry everyone across that" and the players are like "high-five! one less problem to deal with!", then it's not true that you might as well have omitted the whole thing. The aaracokra player got to use his power, and the group got to feel awesome, and that means you're doing a good job as DM.
The other issue is that most campaigns actually don't involve that many pit traps. D&D has a lavish, carefully built combat simulator, and most people that are playing D&D are having combats. If they're not having combats, they might be navigating social challenges, using stealth and trickery to outwit their opponents, or dealing with exploration challenges such as hidden doors, traps, or the vanishing walls and barriers you suggested. The pit traps you mentioned come up seldom enough that it's okay to let the aaracokra be awesome and resolve them.
It sounds like you might be running a home game, and you're expecting to offer the players a larger-than-average number of hazards that can be avoided by flying. If so, it's okay to simply ban aaracokras from your campaign. One sneaky way to do that might be to tell your group that you're playing by Adventurer's League rules; these rules do not allow flying characters at first level.
Best Answer
These are certainly creative, but they are not things the spells are capable of.
Both Frostbite and Ray of Frost specifically 1) target a creature, and 2) cause damage. They do not create large, strong, solid quantities of ice or frost, let alone free-standing or shapeable quantities.
To do that, your player's character need to learn a different spell, because spells do literally only what they say they do.
Your player is definitely demonstrating creativity and I cringe to see that crushed, but how they're trying to bend/break these spells is diametrically the opposite of how the overall game functions. They are effectively trying to be more powerful than they've earned, nullifying the need to grow, earn XP, and learn newer, more powerful spells that do the new things they want to do. They're basically giving themselves power and treasure (which is what new spells are).
There are games that work this way — where you can narrate creative portrayals of magical effects and have them just happen — but those games aren't D&D 5e and they work differently, with different abilities and limitations permitting and gamifying those kinds of creative freedoms. They still have limits, but they're in different parts of how the game works — and D&D 5e for obvious reasons lacks limits in those places, and so has no built-in way to prevent freeform magic from taking over and nullifying large parts of the game if it's added to the PCs' abilities.
D&D 5e is a game about looking at your (limited) personal abilities and resources, looking at the (limiting) environment, and figuring out clever combinations of them in order to overcome those limitations and achieve your goals. Freeform creative magic upends that, and will make the rest of the game kinda break, as its basic motivation loop of striving against challenges, to gain new abilities, and using new abilities to overcome greater challenges will no longer loop.
(That said, you might have fun with that anyway — there is a long, long tradition of bending/breaking games until they are more like the game everyone in the group wishes they were playing — but it only works if everyone in your group wants the game to be that different game. If you're going to let this player run wild with their magic, pause and pay attention to how the other players are feeling, positive or negative, about this change from what they thought they were playing.)