I think that at the end of the day, a definitive statement would (hopefully) stop people arguing about what D&D is. Of course that wouldn't do anything about people arguing about what D&D should be, which, well, is what this thread is all about.
As for the Sorcerer- of course the class should exist. Why wouldn't it? It doesn't make the other caster classes seem less cool. It doesn't come with the baggage of "probably evil dude looming over me", "chained to a money-devouring book", or " probably non-evil dude looming over me" that other full (ish, in the case of the Warlock) casters have.
The only caster class that's equally free of such things is the Bard (arguments about the Bard go elsewhere).
Since D&D doesn't officially recognize "The Gift" (sorry Ed Greenwood), the Sorcerer is still the class for "born with magic" as your go-to. That's not a big deal mechanically, but there it is. Nothing stops you from saying your Wizard, Cleric, or whatever was "born with magic" (subject to DM approval, I suppose), but it's not the default flavor.
Sure, there's an overload of Charisma-based casters in 5e, but that's not the Sorcerer's fault.
So the class has a right to exist, unless you believe "less classes is more", at which point, I could say the following:
Rangers are just Fighters with 1/3 Druid casting and woodland stuff.
Paladins are just Fighters with 1/3 Cleric casting and holy knight stuff.
Bards are just reflavored Arcane Tricksters (1/3 Wizard casting and music stuff).
Warlocks are just Wizards with a different origin (see the Witch Kit from 2e's Complete Wizard's Handbook).
Druids are just Clerics with woodland stuff and some shapeshifting.
Clerics are just Wizards with armor and heals.
So there, we've slimmed the game down to three classes. What was gained? Simplicity? Lower page count?
What was lost? Flavor drained from classes.
Now this isn't to say I think the Sorcerer is fine. I've played a Sorcerer in three editions now (four if we count Essentials, five if we count Pathfinder 1e) and this is what I learned.
3e: getting new spells a level lower sucks. Having to carefully pick and choose new spells at level-up so I always get the most useful one and don't end up with an irrelevant spell choice is not fun.
Pathfinder 1e: as per 3e, but add having to sift through all the Bloodline options to find one that suits the character I want to play and isn't full of weird abilities I'll never use.
4e: feeling like a less useful Wizard and a lackluster Striker.
4essentials: bringing the damage, but with as much fun as Eldritch Blast spamming.
5e: having all the "prepared" casters stealing the best part of my schtick, having to go back to carefully picking and choosing new spells. Having too few Sorcery points to use very conservatively designed Metamagic, or inefficiently doing what every Wizard can do with Arcane Recovery, and having subclass abilities that use my Sorcery points.
BONUS: having my only class feature only come up 5% of the time natively and even then being 50% detrimental (and having to ask "DM may I?" to get my Tides of Chaos back). This is specific to my subclass, I suppose if I'd been Dragon I'd have been better off, save for the fact that Dragon incentivizes me to center on one damage type, and there aren't good spells at each level for all damage types.
With being able to prepare a list of spells and being able to decide which of those you can cast vs. the limited spells known of the Sorcerer, what's the advantage, again? Especially since you can prepare new spells every day?
And let's not even get into the Cleric or the Druid who can freely tap into their entire spell list daily (granted, most Cleric spells suck, so not a huge advantage, but still...).
The Sorcerer isn't irrelevant as a concept, but it's execution may be.