I'm trying to understand your argument, but... it just doesn't make sense
(...)
Now then, let's look at some raw numbers.
Lore Wizard gets Alchemical Casting at 6th level, and at that point has essentially 5 metamagic options.
They have a free, at-will elemental substitution
They have a 1/day alteration of the saving throw
They can burn 1st level slots for +2d10 force damage
They can burn 2nd level slots to cast things with a range of 1 mile
They can burn a 3rd level slot to increase their DC by 2, for every target effected
Oh, and with Arcane recovery, 3 of those spell slot levels can be retrieved, just need a short rest.
And the Sorcerer?
They have 2 metamagics. At 20th level they'll have 4, still one less than your wizard.
-Want to do more damage, 1 point and you can reroll some dice and hope you roll higher.
-Make things harder to save 3 points and you can give one creature disadvantage. Want to do that to more than one target? Too bad, impossible.
-Need more range, single point to double range, but unfortuantely, you took empower and heighten up above and can't use this one.
*Want more points? Burn Spells, 1 pt per level (which makes your 3rd level spell equal to my 3 points for heighten)
*Want more Spell slots? Well, that will cost you, on average of 2 points more that the spells level. So that 3rd level slot you get back with a short rest, costs me 5 of my 6 sorcery points.... which means I only have a single point to work with, I'm losing resources, and you are gaining them back.
Of course you aren't going to burn them all the time, you're going to wait until the right moment, after all, your still a wizard, your identity isn't tied up in all this. You could cast spells as normal and still be a wizard. But when you do decide that investment is worth it, well, you do it better than the guy who sacrificed everything else you have.