Totally late to this thread, so sorry if I repeat. I *like* 5e, but like most versions it has it's limitations. My main beef right now is the low number of spells per day, particularly at high levels, that casters get. I know casters had to be balanced better in this edition than in previous, but the economy of spell casting, particularly for wizards seems to have penned in spell casting a bit much.
You're failing to consider wasted and under-utilized slots. In the classic game, you had a lot of slots at very high level (though you had fewer than in 5e at low level), but you had to memorize into each and every slot exactly the spell you would cast in it. The result was that you would have some spells you cast at less than optimal effect because they were the best thing you had left in the circumstance, and some you didn't cast at all because they never came up or you were saving them. You had all these slots, but you sacrificed some of them for versatility.
In 5e, you use slots to cast spontaneously, so you always cast the best spell that you have prepared when you use a slot at all, and if you prep a spell but turn out not to need at all, you simply spend all your slots on other spells. Slots are only wasted if get a much shorter 'day' than you expected. So you need fewer slots.
Another factor is Concentration. You can't just 'layer' a bunch of buff, damage-mitigation, and mobility spells on your party ahead of a fight, and they come to be expected and 'factored in' to challenges as you level. You have to pick & choose, and the one spell you choose will see you contributing significantly to the whole battle. So, again, you need fewer slots.
Yet another consideration is that fights in 5e are relatively short (relative to classic & 4e fights, not 3e rocket tag), so you may not need as many spells to get you through each fight.
And, of course, you have non-trivial at-will cantrips to fall back on any round that you decide not to use a slot, so conserving slots is an easier decision, and your performance when not casting is at a higher baseline than if you were throwing darts or firing a crossbow or whatever.
And, all of that is relative to 3e or classic D&D, when you did - at high enough level - have more slots. At low levels, in 5e, you actually have /more/ slots than in classic D&D. And, when compared to the last edition of the game, you have
far more daily slots available to casters at all levels. So the immediate trend is not 'fewer slots and better balanced,' it is far more slots, vastly increased versatility, and tenuous balance by protracted 6-8 encounter days enforced by DM Empowerment.
If you feel the caster you're playing 'doesn't have enough slots' that just means you have a good DM.
I'm also not a fan of the "short rest" mechanic which makes healing difficult and also, due to some classes relying on short rests to recuperate abilities like ki and spells (for warlocks) can make it difficult to balance those classes against classes that don't rely on short rests. Too many short rests and they become OP, too few and they are at significant disadvantage.
The same has always been true of characters with all-at-will abilities, like traditional fighters, and the number of encounters/day. 5e requires a longish - 6-8 Encounter/2-3 short-rest 'day' - to balance the classes resources against eachother (and against encounters). It's up to the DM to make that happen - or adjust encounters, introduce uncertainty, manage expectations, "apply DM force," and/or otherwise keep things in balance to the degree & in the way that's best for his campaign.
