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
Spells Copied from Another’s Spellbook or a Scroll:
A wizard can also add a spell to her book whenever she encounters one on a magic scroll or in another wizard’s spellbook. No matter what the spell’s source, the wizard must first decipher the magical writing (see Arcane Magical Writings, above). Next, she must spend a day studying the spell. At the end of the day, she must make a Spellcraft check (DC 15 + spell’s level). A wizard who has specialized in a school of spells gains a +2 bonus on the Spellcraft check if the new spell is from her specialty school. She cannot, however, learn any spells from her prohibited schools. If the check succeeds, the wizard understands the spell and can copy it into her spellbook (see Writing a New Spell into a Spellbook, below). The process leaves a spellbook that was copied from unharmed, but a spell successfully copied from a magic scroll disappears from the parchment.
Page 178 of the 3.5E PHB:
ARCANE MAGICAL WRITINGS
To record an arcane spell in written form, a character uses complex notation that describes the magical forces involved in the spell. The notation constitutes a universal arcane language that wizards have discovered, not invented. The writer uses the same system no matter what her native language or culture. However, each character uses the system in her own way. Another person’s magical writing remains incomprehensible to even the most powerful wizard until she takes time to study and decipher it. To decipher an arcane magical writing (such as a single spell in written form in another’s spellbook or on a scroll), a character must make a Spellcraft check (DC 20 + the spell’s level). If the skill check fails, the character cannot attempt to read that particular spell again until the next day. A read magic spell automatically deciphers a magical writing without a skill check. If the person who created the magical writing is on hand to help the reader, success is also automatic.
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:
LEVEL
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:
Page 35 of the 3.5E DMG:
"Wizards and sorcerers should not cast healing spells, but they should have the best offensive spells. If the spell is flashy or dramatic, it should probably be a wizard/sorcerer spell."
"Clerics are best at spells that deal with alignment and have the best selection of curative and repair spells. They also have the best selection of information-gathering spells, such as commune and divination."
