We have a fundamental disagreement here. I feel(and I know you feel differently) that subclass is where this should be addressed. There's plenty of room there to give a few good non-combat abilities without hurting the main class. The subclass is also where most of the flavor of the class comes from.
Then yeah, we maybe just don't have anything further to say to one another. I have much higher standards for what I expect of classes and find subclasses mostly inadequate to address the underlying gaps in the class itself.
It is worth noting, though, that at the very least you're specifically saying that the first two levels should thus leave Fighters and Rogues
completely high and dry, since (unlike all full-casters except Bard) they have to wait for 3rd level to get their subclass.
Spells are really overrated in 5e. You can't cast many out of combat without gimping yourself in fights. Slots in 5e are really limited. And they are pretty short lived and often come with drawbacks(some very serious). A spellcaster has the ability to be good at all three, but not in the same day.
Even if you're averaging 6 combats a day (which, again, most groups express that that would be an impractical pace), that only means 6 combat spells are needed. Every full caster can do that (and, admittedly, little more) by
3rd level, aka the moment a Fighter or Rogue
get their subclass. By 5th level, when casters are getting access to things like
fireball, the caster has enough mojo to drop a spell every combat and still have three left over. It only gets
worse from there. And, yes, you can certainly argue that 1st-level spells become less valuable for combat (for example), but they usually
do not become less valuable for utility--meaning the Wizard can dedicate most of her high-level slots to combat while still offering extremely strong utility. (And that doesn't even count ritual casting, which blows the whole "spell slots are precious" thing out of the water.)
If you're like a more typical group, where you do roughly 4 combats a day (give or take one) and get 1-2 short rests between them, the full-caster can quite easily have about as many spell slots as the Battle Master has
total expertise dice that day. 5th level Wizard who forgets she has Arcane Recovery: 9 spells. 5th-level Fighter getting two short rests a day: 12 superiority dice. Are spell slots really
that precious? (Spell-recovery features, such as Arcane/Natural Recovery and Harness Divine Power, can potentially let you
exceed the number of expertise dice a BM gets.)