This may be better suited to the other Sorcerer thread. But I really don't feel like typing it all out again. So I'll put it here and see how it goes...If it makes more sense for the other sorcerer thread, feel free to move it.
Note any "you"s or "your"s are the general "you/your" and not directed specifically at the OP or any single poster/replies.
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I am forced to ask the question...How many spells should the Sorcerer have?
Same as the wizard, I suspect, will be the answer I get.
So, the scheme of casters/magic users of D&D the sorcerer-advocates would be "happy" with are: Wizard/Sorcerer #1, i.e., the same except for casting mechanic, followed by cleric, followed by druid...then whomever else?
I don't know. I'm asking. What would make the [apparent vocal minorty] of sorcerer-advocates happy as the "right" number of spells?
To my (and I can certainly hope the designers') mind, Sorcerer's aren't that integral/important/archetypal 'niche" in any way that any other mage/wizard/witch/arcane MU can't be. Nor do they have the legacy/tradition to warrant making them the class who is the "best" at magic [or equivalent].
But...but...spell versatility....So play a wizard if you want the spell list, add "I have magic in me bones" or "I'm a natural with magic/arcane prodigy" or "prophesied spell-weaver" or "you have to be born a witch/wizard" or whatever other special snowflake you need to your fluff. Sure, you carry around a spellbook. It's on your character sheet. Nobody says you have to roleplay using it.
Not to mention, giving the 130 long spell list for Sorcerers a once over, there is no shortage of versatility. Be a blaster. Be an enchanter/fey-blood. Be a thiefy sneaks-alot. Be a diviner. Be an all over the place utility-caster. Can you do as much/as many as the wizard equivalents/specialists? No. You can't. If you want to be "that good", then yes, you need to put some effort into learning some magic. Again, in the hand of the player's choices, as it should be.
But...but...weapons...So, play a bard, warlock, eldritch knight fighter...or take a feat to get proficiency. That is what you want? That's the character concept you have? That's great! Make your choices, as the player, to make happen.
But...but...I don'wanna play another class, a.k.a. I want my melee cake and eat versatility too. I wanna play a Sorrrcerrrerrrr... Then, I can't help you. Because there are ways to get what you claim you want, the game isn't giving you exactly your idea in a neat little package, and you're just being difficult, i.e. whiny entitlement.
It all boils down to: Sorcerers were nothing more than Wizards with [weak] fluff given an alternate spell mechanic.
They were [one of the things done for] WotC's attempt to put their stamp on the game with 3e, by offering a "video-game-esque" spam-caster type that would appeal to (and hopefully draw in some of) that audience. That is all they were/are.
NOW, in 5e, they have been further "specialized." I think that's great!...since there is no chance of them being deleted entirely...at least, now, they sound like they are a little bit different.
Their "limited" spells they know are now an actual limitation that has [at least some] meaning...and that is offering the conceit that the third largest spell list in the game is a "limitation"...you, literally, can not learn anything a wizard can. You are the second-class arcane spell-caster. That's what you get for your "freedom from study" fluff. That's what you are. If that's your [rightful] choice of class...deal with it, e.g. accept it, change it to suit your needs at your table, do nothing but fume, etc...
[EDIT] To the specific question of the OP, in case it isn't obvious...No, I would not permit a sorcerer pc to just pick any spells they want.[/EDIT]
/a bit more ranty than I thought it would sound, but with my sincere legitimate viewpoints