It will make them stronger, but not much

This answer is about Wizards, but I agree that more spells from the same list are not much improvement. Usual Sorcerers take the 15 spells¹ they find best or strongest, so by definition the next 5 will be weaker.
They have the same number of slots, and more importantly, the same number of actions per encounter.

Example: Lightning Bolt

In most situations Fireball is better than Lightning Bolt, as it usually covers more area. It effects more enemies, so most Sorcerers only know the former as they can't afford both.
After this change they might be able to take both, but in the vast majority of the cases, they will still chose Fireball to cast. Only in the few times when the enemy is lined up nicely, or is resistant/immune to fire but not to lightning, will they cast Lightning Bolt. So in about 10% of encounters, they will not lose 50% of their damage (they will lose some damage, as most likely less enemies fit into a line than a sphere).

This comes up to 5%, hardly unbalancing².

Spells from other lists

This is where the idea can go wrong, so you have to examine it on a case-by-case basis:
A twinned Tasha’s Hideous Laughter or heightened Evard's Black Tentacles³ is very powerful, but no metamagic will make Flame Blade great.

This just can't be answered unless we see the whole list for all archetypes, but than it might be too broad.

Try to fit all possible metamagics on the spells, and if it still does not look overpowered, you are fine.

^{1. Sorcerers know 15 spells on level 20.}

^{2. The difference is even less, you could just cast something completely different like Toll the Dead or Haste.}

^{3. I think named spells (Evard's, Tasha's) are usually created stronger, because they are unavailable for Sorcerer's. Consider them a Wizard class feature compensating for no metamagic}

This is Fine

Mechanically, Fire Bolt is far superior to Produce Flame with better range and better damage. For utility, Light far surpasses Produce Flame as a source of visible light at double the radius of effect.

The only thing that Produce Flame can do that the other two cannot is the name of the cantrip itself: it can produce a small amount of fire that persists for the duration. This fire, unlike that of Fire Bolt, cannot light anything on fire however, since in Fifth Edition spells only do what they say they do. The main benefit to this cantrip, then, is that you get a both a source of light and a source of damage from one cantrip, great for druids who only have 2 cantrips at level 1.

Thematically, this is a druid spell, but it doesn't stretch the imagination too far to say that a sorcerer (and especially one with a fire dragon bloodline or some similar origin) could realistically replicate this.