I am working on an alternate sorcerer to accomplish two things, distinguish it more from wizards and make subclasses feel more distinct.
One of my approaches is to do more with sorcery points. I am giving more metamagic as well as subclass specific abilities that use them.
This runs even harder into the sorcerer's resource management problem. I am looking for suggestions on how to provide more sorcerery points to play with without letting a character just using them all for spells.
Is it class-destroying to remove flexible casting and just give a arcane recovery mechanic?
If you want sorcerers to feel distinct from wizards then rather than just sorcery points and more metamagic options, you really need to actually change up the format of how the sorcerer gains and casts spells, like the warlock does.
The warlock's spellcasting is its own system-- small amount of spell slots that refresh on short rests that, when coupled with invocations for additional always-available magic, creates a different type of casting experience. So long as the sorcerer has the exact same spell slot gain and spend as the wizard, bard, cleric, and druid... they will never feel that much different. As the sorcerer is all about internal magic they generate and power through themselves, their magic system should feel more like the monk and less like the cleric, druid, bard, and wizard.
Easiest way to start finding that direction is to go with the spell point path from the DMG. Transfer all the sorcerer slots to spell points and add the sorcery points to the total. Once you have this huge pool of "sorcery points", the player can then cast spells in whatever manner they want. On top of that, if it was me, I'd make every single metamagic option available to the sorcerer (meaning they don't have to choose specific ones.) At that point, everything is about having this internal pool of magical ability castable in all different ways in all various pools of power and strength, unbound to the "rules" that the wizards, clerics, bards, and druids have to follow.
At that point, I suspect that the lower amount of "Spells Known" might not be as much of an issue, as they are gaining many more metamagical abilities to change things up for the spells they do have, and many more sorcery points available to use for those metamagics more often.
Now to be honest... that doesn't really solve your "sub-class" issues to make them distinct from one another. But to me, there's really only one way to solve sorcerer subclass issues and it can't be done through the standard PHB ways-- it has to begin and end at personalized spell lists. Which means going through the effort of creating personalized spell lists for each sorcerer subclass based upon the theme of the subclass.
If you are a storm sorcerer, your spell list should pretty much be filled with storm magic. Including spells that aren't on the traditional sorcerer or wizard lists.
Call Lightning is a must for your spell list. But by the same token... that Storm Sorcerer also shouldn't have access to spells that are blatantly incongruent to its internal pool of storm magic. There is absolutely no reason why a child who was born during a massive storm and was imbued with the Weave as it engulfed him should be able to cast the Disguise Self illusion (even though its on the sorcerer's spell list) So get rid of it. Make up a personalized Storm Sorcerer spell list that only have 8 to 10 spells spells at each level that make sense for a Storm Sorcerer to have.
Because having 17 supposedly different sorcerers, all of whom gained their magic through all manner of different ways... ALL casting
Shield, Mirror Image and Fireball because those are the best spells for a sorcerer to have... pretty much destroys any chance of individuality or distinction between them. The only way to get a Shadow Sorcerer to not take
Shield is by changing their spell list so that
Shield is no longer an option for them to take.
In my new Eberron campaign, one of my players wanted to make a Chronomancy sorcerer (through an aberrant dragonmark). And I did it. And the way I did it was be completely re-writing the spell list for the character and only including those spells that could adequately be fluffed or re-flavored as slowing, stopping, or speeding up time. And anything that could not were not included. No
Burning Hands, Darkvision, or Stinking Cloud for this guy. He still has plenty of good magic, but there's definitely a thematic aspect to him that makes him appear different at the table.