I'd cautiously disagree with that. I think the overall concept of the sorcerer pushes you to pick a themed package of spells, but the limitation in the number of spells known means that you generally want to make sure you have all the major power bases covered first, and there isn't a ton of room to make frivolous picks. Most sorcerers I see have some blend of magic missile, shield, mirror image, fireball, counterspell, and haste right off the bat, possibly swapping some for some of the stronger cleric spells if the sorcerer is a divine soul.
In my ideal world, each sorcerer subclass would have a dedicated small spell list they could cast from freely, much like the 3.5 beguiler, and then get a few extra picks like bardic Magical Secrets. Barring that, I think the class needs some incentivization to gain thematic but not top-tier spells to generate more variety.
(Emphasis mine)
I think this highlights that a problem with the Sorcerer is that people try to play it as a Wizard. "Covering all the major power basis" is really the flexibility expected from a Wizard. The Sorcerer does not have the capabilities to cover that, and if someone tries to follow this approach for choosing known spells, it fails miserably when compared to an actual Wizard.
The fact that the Sorcerer has a large class spells list, only slightly smaller than Wizard, is deceiving. In theory it should be a good thing, it gives more freedom for everyone to decide what spells to choose, but if it leads most players to pick traditional Wizards spells and quickly run out of known spells to give their Sorcerer a unique purpose and identity, then it's a trap.
Maybe the mistake from the designers' part was to actually include stuff like Fireball or Counterspell on the Sorcerer's spells list, it's too good not to pass. Perhaps these "big winner" spells should be given as special abilities of individual subclasses rather than being on the class spells list.
My thoughts on the sorcerer class in 5E has always come down to just a couple things:
1) Every sorcerer PC should have their own specific spell list crafted by the DM based upon the Origin or theme. Spells should come from across all the class lists to craft the most applicable spell list for the sorcerer, but only maybe 8-12 spells per spell level. The reason for this of course being that you remove from all sorcerers the exact same spells that appear on every list and invariably get chosen and cast all the time regardless of Origin or theme. It does not good to have a "Storm Sorcerer" that throws fireball after fireball because fireball is the best 3rd level spell in the game.
2) Every single metamagic is available to the sorcerer. None of this "choose two" crap. The whole point of having a sorcerer (and metamagic) is that because they are infused with magic and can create it spontaneously, they can change it in ways other spellcasters can't. So for my money, that means they should be changing it almost every round, and changing it in all kinds of different ways depending on the circumstance they find themselves in.
The first idea is definitely good. We know that the Sorcerer class was a rushed design because they didn't playtest it publicly, it went straight into the PHB (not counting the early Sorcerer class which was different), they didn't have time to think about a more unique Sorcerer spell list so they mostly used the Wizard list as in previous editions.
I wouldn't want to necessarily single-handedly tailor the spell list to each subclass, but if spells had
tags (like LevelUp is considering to add to the game) then it would be easy to just say "ignore the Sorcerer spell list, pick known spells freely from the PHB as long as they match the tag(s) granted by your subclass".
Idea 2 also has merits. Generally speaking for me it's important that every PC has a certain degree of uniqueness/individuality, so I like whenever a class levels offers a
choice. But exactly which metamagic a Sorcerer can use is not that much characterizing its uniqueness, at least not nearly as much as which spells she knows, so it can be handwaved in order to give more uniqueness to the class as a whole over the Wizard by having it use metamagic more often.
Not sure really if I would go as far as Idea 3 with spell points refresh on a short rest. Eventually, if we accept that the Sorcerer shouldn't really be played as a Wizard but instead focused on a theme, we might want some compensation, but I am not convinced by such a big change. It's also very dependent on adventure pacing, which makes it difficult to apply generally (but this is true for any class that has big short-rest abilities).