People have basically covered all my thoughts as to why separating combat and utility spells wouldn't be good. I just want to explicitly state what some people seem to be hinting at, which is that the original post seems to have a baseline assumption that combat spells are inherently better than non-combat spells. I think this is an artifact of 4e's encounter-based design (as noted above, it's required for encounter balance to have a solid idea of a caster's possible damage output, etc.); 5e has been stated to be moving away from this design ethos and therefore we should see a return to importance of non-damage-dealing spells. Great examples have been given above of how a non-damaging spell can be used to greater effect than a damage-dealer of the same level.
Similarly, Mike Mearls has stated that the guideline for 5e isn't to have perfect encounter balance. It's okay for one PC to dominate a particular encounter, as long as everyone gets a chance to shine over the course of the adventure. For a caster, this could be achieved with a well-placed sleep or burning hands, but also by disintegrating the door that's between the party and freedom, or as suggested above, using comprehend languages to avoid a conflict entirely.
Taking damage spells should absolutely have an opportunity cost as the wizard loses the ability to do anything else. It's a balancing act that should say something about the individual wizard; every wizard shouldn't be made to fit the same pattern.