So oh well it's an unlimited resource I might as well do it. This is something that has been debated to death so I'm not going to go into all the details of why not to have unlimited "minor" magic.
Just to point out the 3.5 damage is effectively twiddling their thumbs as you say. However you are using the opposite argument that they will be twiddling their thumbs because they are not doing 3.5 damage.
That is a totally different beast, actually.
I have no problem with limited magic missiles. I really would like at will magic to use up cheap components etc. Maybe some cheap fokus. Maybe even an unscaled magic missile withut components, but a slightly improved magic missile with a component.
Really, we speak about a fighter doing 1d4+2d8+strength damage with his fists. At-will. So a magic missile that does 1d4+1 damage does not sound reasonable at all at higher levels. It has nothing to do with costing components or beeing really at-will (which i am also no big fan of).
You should regard those failings of the current magic missile as two different problems.
You also should ready my post again:
At-will spells need to be slightly less powerful than the lowest possible spell level you can memorize at any given character level.
IF your 1st level slots fade out, and you cap at 12 spells per day, cantrips should still be useful IF you want at-will magic at all.
IF first level spell slots don´t fade out, 1d4+1 magic missiles are ok, but pretty useless later on.
We don´t know how things are going at higher levels, but I really hope, that memorization is the core of a wizard, meaning, that the highest levels should always be vancian, but to make spell memorization somehow more manageable, his lower level spells/cantrips should be usable more freely...
(always staying well away from the damage, a high level fighter can do at will or well away from the utility a rogue of equal level brings to the table)