I see. I would think that the combination of shield, absorb elements, counterspell, dispel magic, polymorph would make the wizard just as survivable is not moreso vs traps.
Shield isn't that useful unless you have mage armor on and have a dex bonus. Mage armor is 8 hours, so you're casting it 3x day to keep it on constantly. Since I have been forced by bad design to go to one long rest per 6-8 encounters which is usually 3-14 days in game time, the wizard doesn't have enough slots to maintain mage armor 24/7, let alone keep it up and use shield more than once in a while.
So let's assume a 6-8 encounter day in a 24 hour period. To have mage armor up the entire time is 3 of the 4 1st level spells a wizard has, which still leaves only 1 casting of shield which will 99.9% of the time be used in combat, not on a trap. Asborb elements? Do you want to give rid of AC from mage armor or shield? Because you are out of 1st level spells already. Or you can upcast it and be using up higher level slots that could be used on invisibility or something else to cast absorb elements. Boy this wizard is chewing through his spells and he hasn't even attacked yet!
Counterspell and dispel magic are highly situational and useful in combat only. They don't do anything at all for a trap. Traps generate effects, but don't cast spells that can be countered and dispel magic only works on spells that are on objects(such as a light spell on a stone), not traps that generate effects. By RAW it's useless on a trap. Now I would personally let it work to suppress a magical trap, but house rules are house rules and don't really have a place in discussing RAW wizards.
Polymorph isn't going to do much. It might let you turn into something to fly out of a pit trap, if it doesn't cover back up. If you have it on in advance, the trap is going to be a concentration roll, which has a good chance of causing the loss of the spell. It's not like you can be a t-rex or anything that size and be walking down most dungeon hallways.
With retries the wizard will eventually get through up to a 22 DC as well. Retries benefit the Wizard more than the Rogue.
How do retries up to 22 benefit the wizard more than retries up to 30 benefit a rogue?
Late tier 2 I think he has enough slots. At level 5 he has 4,3,3,2,1 slots and the ability to recover up to 5 levels worth of slots, which might look something like 9,3,3,2,1 or 5,5,3,2,1. Use the higher level slots mostly for combat encounters, use the lower level slots more for out of combat and defense. There's plenty of slots to go around.
A few things. First, the first number is cantrips which will be mostly useless and don't actually go down. Actually, thinking about it I think you typoed the first number and are thinking level 9, which makes sense for the 5 levels of recovery

Okay, going with level 9 the wizard is still using up 3 1st level spells just to keep mage armor up so that he has a halfway decent AC. He's still going to get hit a LOT, though, so he will need those other 6 1st level spells for shield and absorb elements in combat.
That leaves 0, 3, 3, 2, 1 to cover combat attacks for 6-8 encounters, which means that if he wants to even try to match the rogue, he's throwing primarily cantrips all day long with maybe 1 or 2 attack spells of higher level. So the rogue can sneak and hide all 24 hours that day. The wizard on the other hand has 3 invisibility spells to cover 3 hours. Less if he gets into combat and gets hit, and he loses out on mirror image by doing so, which is very helpful in keep squishy wizards alive in battle. And knock? It opens one door at the risk of a TPK and uses up a precious invisibility or mirror image slot.
Now we are at 0, 0, 3, 2, 1 and other than some invisibilities to be 1/8 as good as the rogue(3 hours vs. 24), the wizard hasn't done much to match the rogue. Third level gets chewed through using counterspell on enemies usually and maybe a fireball, which means that there aren't a lot of, or even any spells left for things like fly to get up to the places the rogue is climbing to or gaseous form to get past a door.
Now we are at 0, 0, 0, 2, 1 and the wizard has MAYBE cast one spell higher than a cantrip in the 6-8 encounters, and failed miserably so far to match the rogue. He's been sneaky for 1/8 of the time available to the rogue OR for 1/12 of the time and knocked open 1 door. And let's be honest with ourselves here, the last 3 slots are going to be used on offensive combat spells, because the wizard wants to do something other than just spam firebolt.
IMO the defensive tools of a wizard are stronger than the defensive tools of a rogue. The spell capabilities of a tier 3/4 wizard + the wizard's skills will often outperform the rogue at the rogues traditional roles. We can go into a list there but I suspect you know most of them.