Okay so..I'm not going to touch any of the other points, but...
Icebolt is for utility.
lightningbolt is the bread and butter damage of a mage
firebolt is the largedamage+knockback for a mage.
This is not addressing the damage or balance, etc. Just..I wouldn't use icebolt for your comparison, as damage really isn't the 'goal' of icebolt. Its usage comes from being able to have five projectiles loaded up to quickly stun enemies/force them to behave certain ways.
I'm not trying to start any kind of argument over anything here, just.. you might want to use lightningbolt in your examples.
Sadly, LB falls behind even more actually. Aside from the knock down on a cc+2 if there's no other foe in range, or a mass AoE spread for a damage cut, which I don't even begin to know how to read into that for game balance on judging what's better. I haven't added in the elemental masteries, but as I'm sure we're all aware, magic is the most costly in it's own skill set compared to any other set regarding AP. If rank 9 ice bolt with a cc+4 wand doesn't beat a fully upgraded gladius and rank E smash and WM (without even factoring in combat mastery), and rank 9 LB doesn't come close in comparison, then I don't know what to say honestly. "Just rank even more things" to beat low ranks and a single upgraded sword (that you start with so all you have to do is upgrade it over time) is crazy.
One thing I'm noticing that really nails magic in the head is needing 20 int for any effect on the damage. From ranking a few of the bolts to rank 9 (not all of them, just using one at a time as an example) you still fall short of a base +20int by a few int. Meanwhile with some melee and ranged skills, by the time you hit rank 9 you get +2-6 damage. Sure in the end that +5% damage from +100 int adds up, but it really makes the early game feel so low compared to other skill sets. Argh, I don't know what to say about this. Focusing on early game for getting into magic while keeping late game not crazy strong by altering early game. What could even be done?