The Wizard's AC and hp would be a bigger concern than being able to hit and add to the hit point damage of the bad guys.
Of course, this entire thing is mostly moot unless someone is playing with your houserule limiting cantrips.
1) Say my mage has Shocking Grasp as my main damaging cantrip. Usually it is good enough to do what I need when I run low on bigger spells. Then I run into something lightning resistant - suddenly, being capable of contributing in another fashion seems like a good thing.
2) Even better - what if I don't want to take a damaging cantrip? A Mage gets 3-5 cantrips over their career. I could easily see someone wanting to fill up on some of the more useful utility ones, especially if they can feel like they will be good enough at swinging a weapon to still contribute when needed, as opposed to swinging that weapon being completely pointless once past the first few levels.
3) Here's one from experience - the opportunity attack. The scene: The party has nearly finished off a powerful adversary, who is down to the last few hitpoints. On his turn... he flees out the door, with the wizard the only one nearby that can take a swing on him. The wizard swings his weapon, he needs a 20 to hit, the villain escapes. Having at least a chance to hit would make that scene a much more interesting one.