That's also a decent way to handle that. I tend to provide a themed spell list like domain spells, providing 2 additional spells for spell levels 1 through 5. I find that's a decent way to provide sorcerers with relevant spells while giving them flexibility to branch outside their bloodline. I think either option is a good way to handle that.
That may help higher level sorcerers. But Bards, in addition to being full casters with their archetype abilities and bardic inspiration also get better armor and weapon proficiencies and a higher hit die. Besides, classically in 3rd edition the balance between wizards and sorcerers was that wizards got fewer spell slots but had more spells to choose from, whereas sorcerers were more limited in their spell selection, but could cast more often and spontaneously. Now that all casters are spontaneous casters, wizards cast more spells and have more spells to choose from, and sorcerers get metamagic? Metamagic is good, but it doesn't quite go far enough IMO. Especially since more metamagic options only allow you to apply a single metamagic option at a time. Now, with your version where sorcerers get more spells known, it helps the balance a bit at those lower levels. But I feel like more could be done.
I know many prefer bloodline bonus spells vs increases number known. My reasoning to increase number is that a player may still not be able to create a caster they envision.
But more importantly, my point is enforced by the way the spell casters get bonus spells in the PHB.
Casters who can change spells, Clerics, Land Druids, and Paladins can change their spells after a long rest and have already a large number known, up to 25 spells. Adding bonus spells that a player doesn't want doesn't matter. A Bard can just choose what spells he/she wants from any class.
However, take the warlock who has a fixed number of spells known. That class is offered bonus spells a player can take as an option. If they were forced to take the Patron spells, they would have 5 spells freely to choose from. Not enjoyable.
So here's an interesting thing to consider. At level 20, over a short rest a wizard can recover a total of 10 spell slots (likely two 5th level spell slots). If using flexible casting to create spell slots, a 20th level sorcerer can create two 5th level spell slots and one 4th level spell slot. Sorcerers get a bit more out of the deal since this pool is split between creating spell slots and metamagic. Also, the spell conversion to create spell slots with flexible casting is the exact same as what is used for the spell point variant in the DMG.
Lets assume both wizards and sorcerers were using the spell point system. By level 20, both would get 133 spell points. Based on this system, a wizard using Arcane Recovery would recover 14 spell points. So in an adventuring day, a Wizard gets a total of 147 spell points to use on spells. They only have to use that resource for spells.
Now what if we said that sorcerers just skip all that. Their power comes in metamagic AND flexibility of spell slots. They get a single resource of Spell Points, and it increases by 20 (1 per level). Unlike other classes using spell points, they gain the ability to create a max of two 6th level spell slots, two 7th level spell slots, and one of each for 8th and 9th. At this point, I don't know that sorcerers need an equivalent to spell master or signature spell. They have a ton of spell points to give them access to more high level spell slots, and flexibility to use metamagic when it benefits. As all casters are spontaneous casters, the sorcerer returns to the flexibility and raw power that it represented in previous editions. If your sorcerer wants to eschew metamagic and just cast continuous spells, they can bring the fire power. If they need to adapt their magic, they can use the metamagic options.
I tried pooling Sorcery Points and Spell Points. The negative is that you regain Sorcery Points after a long rest only. You can homebrew the recovery, but it would still be a low number and that is what I still found frustarting. Arcane Recovery is once per long rest. Separating the points allows you to recover Sorcery Points after each short rest.
1. Quickening to cast cantrips for damage
2. or Twinning a spell so you can affect 2 creatures you may not normally be allowed to do or Twinning to effect another creature without needing to use a higher spell slot, thus less spell points, is great.
If we assume WoTC got the Monk correct with regaining Ki after each short rest, then by separating Sorcery Points from spell slots should allow a Sorcerer regaining them after a short rest be balanced.
Now this makes Sorcerous Restoration a bit more worthwhile. Though I might change it to this:
Sorcerous Restoration
At 20th level, you regain a number of spell points equal to twice your Charisma modifier whenever you finish a short rest. This cannot bring you above your normal maximum spell point total.
Mind you I am not sure if any of this would be balanced and have not thoroughly thought through the potential uses/abuses. But it is interesting to consider. Also, important to note that in my Homebrew, the Signature Spell ability works more like Spell Mastery, allowing two 3rd level spells to be cast at their lowest spell level without consuming a spell slot at will.
We have different options for 20th level:
Lowering the cost of all metamagics with a cost greater than 2 by 1.
Roll initiative and 0 SP, gain 5 SP
etc.
