I personally think there is no real difference between a 'class-exclusive spell' and a 'class feature' except for the number of times it can be used (class features would usually be X times per long rest, class spells would be as many times as you'd like based on available spell slots.) So thinking one method of counting is better or more appropriate than the other is not something I believe. Both are fine ways of counting.
I mean look at it this way... a character at 12th level will be throwing around their high-level spells all the time, and could easily have days where they have left up to like a half-dozen 1st and 2nd level spell slots on the table unused because they were not needed. Is there thus any reason why a different so-called "class feature" couldn't be using those unused slots, rather than having its own completely different counting system of how many times it can be used per day? For me personally... there is nothing inherently wrong with using one or the other. So I don't dismiss the option out of hand just because "Ew! Spells!"
one reason that some spells should become class features is to remove penalties that comes with using spells. Spell components, silence, counterspell, etc.
And I agree with unspent slots, that is why the new exclusive sorcerer spells should be innate abilities that can be boosted with using spell slots.
Sorcerers Burst, this needs buffing or removal for just an extra cantrip slot. Making it d8 might help this along, or better yet 2d4 with 2d4 increase in cantrip power level, that might see more explosive dice,
Also add that you can add d8(or 2d4) for every spell slot you spend when casting this cantrip
Sorcerers Vitality: this is just bad.
Rework: when you cast a spell of 1st level or higher, you can as a reaction use part of the spells magic to heal yourself. Heal for 2d4 HP per spell level. If used with 3rd level spell or higher end Blinded, Deafened or Poisoned condition also.
Arcane eruption, this is mostly on, but I would like this to also be an innate ability, that is usable at will.
rework:
Action to use,
Deal 1d6 of damage in 5ft radius.
You can use a spell slot to increase damage by 2d6 and radius by 5ft
Sorcery Incarnate: this is mostly horrible:
rework:
Bonus action, usable once per Long rest
duration: 1 minute, uses concentration as in concentrating on a spell.
1. Gain 3 Sorcery points when you use this ability.
2. you can concentrate on 3 spells at a time(this ability uses 1 of those 3). if you fail Con save, you lose all spells.
3. You spell attacks have advantage on attacks.
4. One target of your spells have disadvantage on saving throws vs your spells.
5. You can use 2 metamagic options on your spells.
you can use this ability again if you spend 5th level spell slot or higher.