Two things. Your alternate rest system does nerf casters some in that their long duration spells don't last for as much of the adventuring period between rests. Mage Armor doesn't need kept up constantly, just in the part of the adventuring day where you are most likely to have encounters.
I know. I've created a work around for that and give casters back 2 spells a night. That seems to be too many, though and next campaign I will probably reduce it to 1. And there isn't a part of the adventuring day that is most likely to have encounters. You adventure for 16 hours and when resting monsters can and often do wander in when you are in a hostile area, which any area with 6-8 encounters in a 24 hours period is.
Maybe instead of making assumptions you should ask how those that believe the wizard is OP would play such a wizard.
No. 6-8 encounters in a 24 hour period is the expected number of encounters, so that's what I will assume. If they are playing less, then it's their fault the wizard is OP. Now if you're talking about the mage armor, you mentioned survivability and not having that AC makes the wizard squishier than a sponge. Especially if the wizard loses initiative or is surprised
Do traps not use magic/spells?
They do not cast them, no. Counterspell cannot stop any spell that was not cast. Nor can the wizard stop any spell he cannot see being cast and traps do not have any V, S or M to alert the wizard in any case.
I'm not sure where you get dispel magic cannot dispel traps from?
The rules. Dispel Magic can dispel a spell ON an person, object or magical effect, not a magical object like a trap. So you could dispel the light spell cast on a coin, but could not dispel a wand of fireballs. You could dispel the polymorph you got hit with when the trap triggered, if you can cast spells in the new form, but not prior to that.
You are technically right on counterpsell though. 5e does require it to be a creature casting a spell within 60ft. We had always ran that it could counter trap spells but that would be a houserule (though possibly a fairly common one).
Creature isn't really the relevant part. Traps do not use V, S or M, so by the time you know something is happening it's too late. The fireball or whatever is already heading towards you. You have to be able to see the spell being cast
Polymorph gives you more hp to take trap hits than the rogue ever dreamed of having.
First, there's a good chance it's for one trap, then polymorph leaves if you fail the concentration effect. Second, the rogue has evasion, so that fireball above is doing half to no damage at all to the rogue, and half to full damage to the wizard. Probably full since wizards don't get dex save proficiency and have lowish dex, unlike rogues who have high dex and proficiency. Those same saves avoid most mechanical traps as well. The wizard better have double or more of the rogue's hit points if he wants to make that claim. The rogue will be taking 0 damage a lot while the wizard is taking full, running the wizard down to 0 long before the rogue goes to 0. Plus, there's still the first problem of maintaining concentration.
Just out of curiosity, what form is the wizard taking for this exploration trip?
Because if you can retry till you succeed (up to your max roll) then for anything lower than that it doesn't matter if you get unlimited retries.
And for anything more the rogue is better. So at best the wizard is equal(if all rolls are 22 or less) and more likely the rogue is better.
Yea it should have said level 9. But again you are making unfavorable assumptions for how I would play a wizard and that likely drives the reason you don't view them as OP.
So what spells do you use to be better than the rogue and at the same time use both defensive magic and offensive magic higher than a cantrip in 6-8 combats?