Under RAW, every sourcebook is created equally. There is no preference to core over WOTC splats. Therefore, "choice" under RAW implies a choice from everything available
You'll need to show me that in Raw. I did find this on page 6 of the DMG:
Choose the rule that you like the best, then stick with it for the
rest of the campaign. Consistency is a critical aspect of rules
adjudication.
That suggests that choosing the "rule" the DM like best allows the DM to disallow splat books or even spells as the DM sees fit. Splat books are "supplemental" to core books.
Absolutely, that is a house rule.
A "house rule" is a deviation from the official rules. Making decisions about what
is available in your campaign is required by the official rules. It is not a deviation from the rules. There is no official rule that says everything that exists in any book is always available to any player. In fact the rules state and encourage the opposite to achieve balance.
There is a categorical difference between saying a spell doesn't exist versus deciding the player doesn't have access to a certain spell due to the campaign setting.
RAW does not specify the type of research that must be done.
yeah, I don't think RAW needs to spell out that if you're researching rubber duckies, you're not going to invent an airplane. Or that you can't research an airplane if no one in your campaign knows what it is or has ever seen one in action.
RAW does not specify the type of research that must be done. Maybe the wiz can figure out the spells on their own as they experiment?
Except that the PHB specifically says the Wizard's dable in "minor magic." I don't think Greater Teleportation constitutes "minor magic"
In any case, the bottom line is that restrictions based on a non-RAW campaign setting are, by definition, house rules.
What exactly is a Non-Raw campaign setting? Here's what DMG says on Page 6
Every Dungeon Master is the creator of his or her own campaign
world. Whether you use the G
REYHAWK® setting (the standard
D&D campaign setting) or another published setting for the D&D
game, such as the
FORGOTTEN REALMS® Campaign Setting, it’s still
your world.
The setting is more than just a backdrop for adventures, although
it’s that too. The setting is everything in the fictional world
except for the PCs and the adventure plot
Emphasis added.
Even if you interpret that to mean you
have to use a published campaign setting, none of the ones I've read tell you what spells are and are not available.
I did find this little tidbit in the PHB p 179.
With the DM’s permission, sorcerers and bards can also select the spells theygain from new and unusual spells that they have gained some understanding of (see Spells in the sorcerer description, page 54).
Emphasis Added.
Even if we concede the Sorc/Bard gets any spell in the PHB, this rule explicitly seems to give the DM discretion over any other source for spells.
For some reason, you seem to take offense at "house rules."
Offense? No. But the label is incorrect and seems to be thrown around to undermine the fact that the balance issue ...really isn't there in terms of how the game is supposed to be run. If people say there is a way to deal with X problem and the response is "oh that's house ruling," that's tantamount to saying, no, you haven't solved the problem.
It is a core principal in D&D that the DM's take actions to balance the game. If DM's shirk that responsibility, it is invalid to say things are unbalanced while ignoring the most crucial instrument designed to enforce balance.