It's a bug, although it should be a feature. 5E removing the Wizard's ability to learn any spell always irked me. It's going to be fixed eventually, but I will love it for as long as it lasts.
Wizards have never been able to learn any spells they want. They have a dedicated Arcane spell list. This was how it was in table top or any of the games, like the original BGs (2e ADnD), and Neverwinter Nights 1 & 2 (3.0e, 3.5e).
What 5E
HAS changed, is the splitting of the Sorcerer and Wizard spell lists. In 3/3.5e Sorcerers and Wizards shared the same spell list. This is no longer the case in 5e (Wizards have a larger and better spell list).
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. 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).
Now, this isn't really a big deal, since the Wizard spell list is, with a few exceptions, better than the other spell lists. But it is a thing that they've always been able to do and they can't anymore, and it makes me sad.
THIS IS 100% false!
You are spreading complete lies mixed with actual game mechanics to win an argument. The argument is about Larians inability to see how stupid it is for Wizards to use a Cleric spells list.
In 2nd edition called ADnD as well as 3.0 3.5 4.0 and 5.0 Wizards have their own CLASS LIST. You can copy any spell from a scroll or other sources as long at is is on your CLASS SPELL LIST and you meet the requirements. The rule is not always written within copying a scroll it uses the universal rule under "LEARNING NEW SPELLS and or GAINING SPELLS" There is usually a chapter before the spell list in all editions. That must be read or information like this kills game balance.
Why would anyone playtesting printed systems ever allow what you just suggested. What would be the point of separating the damage from d6 and d8 from arcane and divine? What would be the purpose of the classes if there was unified lists mechanics and powers? They did the work to seperate the damage and the intent of all spells with the appropriate spell list in every edition. You must have been a player with a game master who didnt like to do his homework.
Please stop spreading misinformation about tabletop rules as written. Those guys work way to hard on the mechanics of their systems to not have it valued.
https://adnd2e.fandom.com/wiki/PHB_Spell_ListsThat was adnd
here is 5.o
"Copying a Spell into the Book. When you find a
wizard spell of 1st level or higher, you can add it to your spellbook if it is of a spell level you can prepare and if you can spare the time to decipher and copy it."
http://www.d20srd.org/srd/magicOverview/arcaneSpells.htm#arcaneMagicalWritingsI could post Pathfinder 1st and 2nd edition that do the same things But I think I proved the point. There is a reason you have never seen this anywhere else other than I guess YOUR table. It is not cause you are the ONLY one reading it right.... it means... you are wrong.
Other than that enjoy the game and have fun playing and stuff. I hope this didnt come off harsh my goal was to help. But english is hard.