Tomato tomato. There were only spontaneous spells known and non-spontaneous spells prepared.
Sure, but the important part was spontaneous magic. Vancian magic is a frikkin' pain to deal with, and the sorcerer offered an alternative (albeit underpowered because they were conservative in balancing it). Also, almost no fictional portrayals of spellcasters that aren't based on D&D or a derivative, or the actual Dying Earth books by Jack Vance, have Vancian casting.
I'd guess it's actually more common to have entirely spell-less magic in fiction, and instead have some kind of freeform system based on various aspects.
This happens if and only if you restrict the number of spells known so that a spells prepared caster can prepare as many spells as a spells known caster can know. If you do that then yes it's worse because spells prepared can do literally everything spells known can and more.
The full casters in 5e are bard, cleric, druid, sorcerer and wizard (and sort of warlock, but they're weird so we're ignoring them). 5e wizard and druid gets level + stat bonus spells prepared. So does the cleric, but they also get two fixed additional spells at each spell level up to 5 from their domain (so basically level*2 + stat bonus until level 10).
The bard for the most part has level+3 or level+4 spells known (level+2 at level 20, but we can ignore that). That's pretty close to where a wizard or druid is, but with the disadvantage of not being able to swap them out. But the poor sorcerer starts out at level+1 up until 11th level, at which point they only add 1 spell every other level. That is
really bad.
And looking at the half-casters, paladins have level/2 + stat bonus,
and get 2 more per spell level for their Oath. Rangers have level/2+1 spells known, and don't inherently get more from their sub-class. Many of the later sub-classes do give one spell known per spell level (but not the ones in the PHB), and the alternate version of Primal Awareness gives an additional one per spell level, which still puts them below a paladin's spells prepared (unless the paladin only has a +1 or lower Charisma bonus).
So, I guess in practice you could balance spells known against spells prepared by juggling the numbers. In practice, that's not what happens, and instead prepared casters have as many or more spells available as known casters.
The 5e PHB went a step further. On average the Spells Known casters knew approximately two spells per spell level they had of levels 1-5 while the spells prepared casters could prepare three spells per spell level. This made Spells Prepared casters awful. And lead to people hating Spells Prepared because WotC hamstrung almost all the Spells Prepared classes.
I think your last two sentences are supposed to refer to Spells Known casters, because otherwise they make no sense.
There is nothing in the concept of Spells Known that says that you should know fewer spells than a spells caster can prepare.
Right. But given equal numbers, spells known is inferior to spells prepared, because a prepared caster can prepare for different circumstances while a known caster has a fixed number of spells available, so they have to pick the most generically useful ones. And the numbers
aren't equal in practice – they're skewed in favor of prepared casters.