If "having a torch" is the answer to a challenge, that's not really a challenge.
The dark nature of dungeons is one of the difficulties of that environment. Torches require a free hand to hold and can be blown out by a gust of wind. The wizard's light cantrip makes darkness a non-issue.
It's like having an automatic "warmth" ability in arctic areas or "cooling" ability in the desert. It negates some of what makes the environment difficult.
End of the world issue? No... but it does take away some of what makes low level dungeon crawling challenging. Not everyone likes that sort of thing, but some do.
Bolded part critical. Wizards should not generally be good at using melee weapons.
Yup. They shouldn't be good in melee, period. Shocking grasp is way too good. The damage is comparable to a longsword. If the target is in metal armor, the cantrip is better than a longsword.
If an at-will magic attack is needed for flavor (personally I don't think it is, but a significant number of people seem to like it), I think it should be on par with a dagger or quarterstaff.
No so in 4E, unlikely to be so in 5E. "Many" traps can be overcome with a hand that can apply a very small amount of pressure?
Mage Hand lets a character open doors, chests, etc. from a distance without touching the object. Poisoned needles, scything blades, and other common chest and door traps can be avoided.
Mage Hand can lift 10 lbs and manipulate small objects. 10 lbs. of force is a pretty good shove. Applying that 10 lbs. of force to a small area (since it can be used to manipulate small objects), say 1 square inch, an that's a strong poke.
Mage Hand can't overcome every trap, but it can overcome a lot of them.
Like a fighter "spamming" a grab or grapple, it's trading an action for an action. No biggie.
Except that the Ray of Frost has no save and can be used safely from range. If you have more than one wizard in the party (or more than one character with at least one level in wizard) they can each spam Ray of Frost each round. As soon as one ray hits, the party is free to pelt the monster with ranged attacks for the rest of the round. Basically, the monster is stun-locked. If it doesn't have a ranged attack handy, it will certainly die.
If the multi-classing rules are anything like the 3e multiclass rules, I can see a lot of characters, especially rogues, taking one level in wizard just for the cantrips.