I don't know if the spell system needs an overhaul. Again, I don't think there's a huge issue, but that's also b/c I am willing and able to engage in serious optimization to make my non-casters work out.
One thing is the resource mechanic to begin with really. With how spell slots work, each level adds a new array of options, but the earlier slots are all still there, and for the best spells, they do not grow significantly obsolete. Using your newer spells do not hinder your ability to pull an early nuke out of your pocket, nor does using the low level spells in bulk do anything about your general energy.
Either you do what they were trying ham handedly with the spell CL caps, or you can merge and streamline the magic mechanic.
I don't think I understand what you're saying here. My point was that I can build non-spellcasting characters that can readily compete with pretty heavily optimized spellcasting ones. I'm not saying it's easy or it isn't a lot of work, it just so happens that I (and really I mean to include everyone in the 3 groups I regularly play with) are used to doing that anyway. So, the game balance concern isn't as dire to me, in effect, as they are by just reading the rules. That's due to some combination of gentleman's agreement and optimization.
That being said, lower level spells
should become less effective as you go up in levels. Generally, a 1st level spell is "supposed to" be a less impressive use of your limited combat actions than a 5th level spell. That's not to say you won't find reasons to cast your 1st level ones -- sometimes that's the effect you're really looking for and the closest thing you have memorized is a low level spell. Or, sometimes the extra oomph from the higher level just isn't worth it: a lot of higher level spells do the same damage as lower level ones, but to multiple targets, and if there aren't those targets handy then you'll opt for the lower level spell.
Now, I said "supposed to" b/c naturally there are some spells that are just really good regardless. I think these might be overstated. Grease is probably a great example, but even then it
does get less useful: at higher levels more opponents can fly or teleport or just have high enough Dex scores to make the Balance check untrained. Solid Fog might be another good example along these lines -- it doesn't lose much effectiveness as the game wears on. Although it's also a reasonably high level spell (4th), so I'm less discomfited by it.
That being said, to the extent that a spell doesn't lose much in the way of effectiveness as the game progresses, that might be an indication that it is "broken," and should probably be changed or excised (in this I am again in agreement with Midnight_v's post a few ones up).
One final thing directly addressing the question: you need multiple encounters before "resting." Without a lot of encounters, spellcasters don't have to manage their resources, and the "I can do this all day" guys are just left in the dust b/c the spellcasters can use their most powerful options all the time. It would take some work to rebalance things if you essentially get rid of the resource issues for spellcasters. And, don't jump on me and tell me that a 12th level Wizard will never ever run out of spells. That's largely true, the question is how many of his 5th and 6th level spells he has to sling for every encounter.