In terms of video games, you are correct. In every DnD video game I've played, at least, spell lists were always sovereign.
In terms of tabletop, you are not. 4E didn't have spells, so I'm not talking about that. In 3E/3.5, Wizards could learn any spell if they found a written copy and succeeded a Spellcraft check.
I disagree. The 3/3.5e "Wizards can learn any spells" interpretation came from picking apart non-specific wording in the Player's Handbook - it's more of a loophole than intentional ruling. Learning also doesn't mean the same as actually being able to cast the spell.
Page 179 of the 3.5E PHB
Page 178 of the 3.5E PHB:
Highlights are mine. While it never outright states that spells must be learned from the Wiz/Sorc list, the intention is arguably there with the multiple references to "Arcane" Writing. Regardless, even IF wizards can add divine magic into their spellbooks, they cannot cast it per the PHB
, which states:
Page 56 of the 3.5E PHB:
A wizard casts arcane spells (the same type of spells available to sorcerers and bards), which are drawn from the sorcerer/wizard spell list (page 192)
Page 172 of the 3.5E PHB:
The next line of a spell description gives the spell’s level, a number between 0 and 9 that defines the spell’s relative power. This number is preceded by an abbreviation for the class whose members can cast the spell. The Level entry also indicates whether a spell is a domain spell and, if so, what its domain and its level as a domain spell are. A spell’s level affects the DC for any save allowed against the effect. "
The note about Sorcerer/Wizard spells is extra important
because Bards in 3.5e do have cure spells that are classified as Arcane. Furthermore, if your class abbreviation isn't in the spell description, you can't cast it.
In 2E and earlier, Wizards could research new spells that weren't on their spell list. Any spell that was currently in the game was considered a balanced option because it already existed, so by default Wizards could "research" Cure Light Wounds and Holy Word. (Wizards could also research new spells in 3rd, but that was entirely for the purpose of creating new spells since they could already learn non-Wizard spells another way).
Wizards can research and create new spells in 3/3.5, but the DMG went out of their way to state their intentions - limitations of what spells each class should have. From the "Creating New Spells" section of the DMG: