So an idea for a homebrew class: a sort of petty wizard class, one that collects spells like mad but gives up getting to the crazy high tiers of magic. They get half caster progression, but twice as many low level spell slots. They would also get cantrips, and more of them. And they can copy low level spells/cantrips from classes they come in contact with aside from wizard. This might still be tied to a spellbook of some kind. 

Their schtick would be to throw in some kind of action surge like mechanic that lets them chain cast these lower tier spells at higher levels to stay balanced, and maybe a "proficiency modifier times per long rest" quickened spell cantrip casting. 

Does this sound like a viable class concept? 

Maybe at low levels, but even allowing multiple leveled spells per turn, it will take a lot of fireballs to match a meteor swarm. 
Even with upcasting, if they don’t have higher level slots, they’ll have a hard cap on how much they can output that seems like it would make them weaker in T3 and 4.

However, they’d risk being pretty OP in T1 and 2 by being able to cast a lot more. With most campaigns ending low levels, they might be very popular, actually. 

Seems like MC wizard/warlock would provide pretty much these exact things. Add a couple levels of MC fighter if you want an Action Surge.

It's also an awful lot like artificer, considering their Spell-Storing Item is effectively a whole bunch of extra low-level slots.

I just don't think this would warrant a class when there's already a way to get most or all of the way there with what we currently have.

I also agree with Xalthu that the way spell progression works, you can't "make up" for high level slots with more low level slots. A lot of high level spells aren't just damage, but they do crazy things that solve problems that no number of lower level spells could handle. In the later tiers, if you don't have high level spells, you need something besides spellcasting if you want to pull your weight.