Yes. And in exchange for that, they get fewer spells and a
significantly worse spell list. Remember: even at peak efficiency, a Sorcerer can't really keep up with Arcane Recovery. And if they use even a
single metamagic, they definitely can't.
Keep in mind, though, that bloodline abilities are things like "free
mage armor and +1 hit point/level" or "cancel out advantage/disadvantage a few times a day" or "get advantage on one roll, but now the DM can troll you." It isn't until you get to very high levels--levels I know you, personally, have many many times argued almost no one actually reaches or plays--that you get actually
strong features, like flight, or (effectively) getting mini-crits on spell damage, or bonus-action teleporting between shadows.
Nobody is getting particularly powerful features in the first 6ish levels.
Don't get me wrong, the Wizard
is badly-made, if one cares about having mechanics that actually convey theme; it puts far too many eggs in the "cast more spells" basket and far too few in the "be an academic who does research to advance the frontiers of magic" basket...as in, absolutely none in the latter. There's
no mechanic in the entirety of the Wizard class that actually does what the class's flavor says. You don't do research--ever. In that sense, Wizard is
worse than Warlock by the standard
@Crimson Longinus has used (which I do not; I am simply noting the problem): at least the Warlock's problem is simply that a Big Event is in the past. The Wizard is
supposed to have this happen all throughout their career, but it is literally never actually a thing the Wizard personally does. All "research" is handled off-camera, presumed, implied. And plagiarizing others' research notes, even with payment,
isn't research, it's simply copying.
Subclasses aren't as impotent as you imply, of course. Diviner, Transmuter, Evoker, and (with a DM that isn't antagonistic) Illusionist are all powerful in their own right. But they could be significantly better.
Further, you're just wrong about sharing so much with Sorcerer in terms of spell lists. Using just the core books (not even looking at Acquisitions Inc. or the various Critical Role books etc.), the Wizard has 23 totally unique spells (exclusively Wizard, no one else gets them except by being part-Wizard, e.g. EK/AT, or taking a feat), while the Sorcerer has ONE signature spell:
chaos bolt. Meanwhile, if we look at spells Wizards can cast but Sorcerers can't, there's a further 96 spells that aren't Wizard specific but which can't be cast by Sorcerers (for a total of 119 spells Wizards can cast that Sorcerers can't); conversely, there's a grand total of
eight spells (counting
chaos bolt) that a Sorcerer can cast that a Wizard can't.
The Sorcerer has a spell list containing all of 218 spells. The Wizard? 329. 111 more spells. More than a third of all Wizard spells can't be cast by Sorcerers--or, if you prefer, Wizards have access to 50% more spells than Sorcerers do. (Oh, and just in case you care: exactly
one of those "Wizard but not Sorcerer" spells is a cantrip.)
Finally, adding in the other supplements/official collaborations/etc. doesn't change this--except to make a bigger gap in favor of Wizards (366 Wizard spells, 244 Sorcerer. The gap has increased to 122.)
Of course you do. Why wouldn't you? Even the Wizard--the one character that
actually can (almost) learn All The Spells And Also All Of Them--has to spend money to do so. It's a risk, a danger, to take spells that end up being useless. Every spellcaster is always encouraged to only take those spells that are most worth taking, and the spellcasters who get fewer spells per day are the ones
most encouraged to pick only the best, most-versatile, most-effective spells.
And, of course, every spell level has a set of them.