I'm working with a player who has a homebrew wizard subclass and we were discussing the possibility of giving it a list of spells that was automatically learned and prepared for this class. We realized that this would be a lot like the domain spells from cleric subclasses. So, what would be the balance implications of letting a wizard subclass have more prepared spells, similar to the way in which cleric domains do?
I want to point out quickly that having prepared spells is only one aspect of cleric domain spells. They also can grant access to spells that would otherwise be unavailable to the cleric.
The short version of the answer is:
It would make the subclass more powerful.
Additional prepared spells makes the Wizard more capable in handling a potential situation.
I think most consensus is that the Wizard class is a fairly strong class already. With the possible caveat of suffering more growing pains at low levels due to low hp.
The slightly longer version is:
The amount of power / utility it grants to the Wizard is directly related to what spells you are selecting to be always prepared. Giving them access to spells outside of their default spell list for example is a large increase in power. Giving the prepared spells which are almost always prepared anyways (shield, fireball and other must-haves) effectively just gives them extra prepared spells which gives them a strong bit of options. The lowest increase of power is if you grant them rarely prepared niche use spells. Having skywrite at your disposal at all times likely will not change the outcome of many scenarios.
You need to determine if this is a concern. The fact is, no matter how well intentioned, most tables have power differences between their party members. Finding some perfect balance is usually a much less important than engaging your players. If these extra spells makes a player feel better connected, and does not detract from other players enjoyment. Then its a good change. Is there a compelling lore / story / RP reason this subclass would grant a handful of spells always at the ready? If there is, you should probably include it.