And a good method of balance would be?
My opinion?
By making the mechanics support the fluff. Supposedly, magic is difficult to control, takes time to master, and using the body for a conduit of supernatural energy is stressful. In
one of the other games I play
this is represented by having spellcasting actually take a toll on your body. You spend fatigue points to cast a spell; being low on fatigue points (as the name might suggest) tires you. If you're out of FP, you may still attempt to cast, but doing so saps your HP instead. Thus it is possible to push beyond your normal limits, but doing so might seriously harm or kill you.
This is not without precedent in D&D. 3rd Edition used the concept of backlash for epic spellcasting; it seems reasonable that such a system could be used with lower level casting as well. The lower level spells would simply be safer and come with less risk; the more difficult (high level/high cost) the spell, the more risk.
This idea need not be uniformly applied. Different styles of casting might have different ups and downs. For example, a wizard (if I remember my 3rd Edition correctly) will know more spells than a sorcerer; however, the wizard is casting through learned ability instead of natural ability, so wizards would use the system as is. On the other hand, sorcerers might have certain spells with which they have less risk -this might be determined by bloodline. A warlock would have less risk with the domain (yep, I'd treat warlocks as an arcane cleric of sorts) granted by their patron, but they'd be required to abide by the tenets of their contract.
The same idea can be used (to some extent) with non-magic classes as well. Spending a fatigue point could allow you to put extra oomph into a sword swing; sustain running over a long distance during a chase scene; draw upon your intestinal fortitude to power open a door as its being held shut by wizard's spell, and a variety of other things. I've spoke about this idea before in a different thread.
That idea of points also has been used in D&D. 4th Edition Psionics uses power points. Perhaps 5E non-caster classes could operate in a way which is similar to Essentials, but with the ability to spend FP to get great effect from their natural abilities.
The answer is right there in the fluff of the game. Why not give a more coherent relationship to fluff and crunch? I'm hardly an expert, but it seems more balanced than the current approach, and it would also create a more consistent in-game narrative.
edit: Also, powerful spells should take a little more time to pull off. A simple magic missile might be easy and take only a minor incantation and a flick of the wrist. Calling down a lightning storm upon a battlefield might take multiple turns. Extremely powerful spells such as raise dead and/or wish might require rituals and multiple casters acting together.