The default wizard gains two new spells to add to their spellbooks per level. It's my contention that this isn't enough for several reasons.
The first reason is that the primary benefit of playing a wizard is spell versatility. The sorcerer focuses on attack/defence, the warlock focuses mostly on attack, and the bard and cleric are all about buffing/debuffing and throwing a bit of attack/defence in when they can. But the wizard is the one who can tailor themselves to the environment and always has that ritual or utility spell in their back pocket to overcome an obstacle or gain an advantage or learn something about the situation.
With the above argument in mind, I come to my second reason that the limit isn't enough because of the nature of gaining spells to add to a spellbook beyond that limit. Random treasure tends to have very few spell scrolls and never has spellbooks. Published campaigns often have very few spellbooks, if at all, and even if they do they tend to be very hard to get and/or easy to miss. That essentially puts your primary class benefit into the hand of fickle fate, or the generosity of the DM catering treasure to your requirements, both of which are not, as far as I'm concerned, satisfactory components of a core system aspect of a class.
The last reason is that if you go through the spell list and choose spells across 20 levels, the system encourages you to select 8 spells of 1st level, and then 4 spells of each level thereafter. Looking through the list, if you only choose utility spells, you're left severely wanting for attack/defence options, and vice versa. And if you compromise and choose a mix, you're essentially lessening one of the best aspects of being a wizard, that of utility spells. Even if you go against the formula I stated, you're still left in that conundrum of losing out on part of the reason to even choose to play a wizard, or being effective in combat.
And all that isn't even mentioning how your core ability is the dumpstat of this edition. I would argue that this limit should be increased to 3 per level instead of just 2. That mitigates all the above issues while still requiring some reliance on luck or DM fiat.
The first reason is that the primary benefit of playing a wizard is spell versatility. The sorcerer focuses on attack/defence, the warlock focuses mostly on attack, and the bard and cleric are all about buffing/debuffing and throwing a bit of attack/defence in when they can. But the wizard is the one who can tailor themselves to the environment and always has that ritual or utility spell in their back pocket to overcome an obstacle or gain an advantage or learn something about the situation.
With the above argument in mind, I come to my second reason that the limit isn't enough because of the nature of gaining spells to add to a spellbook beyond that limit. Random treasure tends to have very few spell scrolls and never has spellbooks. Published campaigns often have very few spellbooks, if at all, and even if they do they tend to be very hard to get and/or easy to miss. That essentially puts your primary class benefit into the hand of fickle fate, or the generosity of the DM catering treasure to your requirements, both of which are not, as far as I'm concerned, satisfactory components of a core system aspect of a class.
The last reason is that if you go through the spell list and choose spells across 20 levels, the system encourages you to select 8 spells of 1st level, and then 4 spells of each level thereafter. Looking through the list, if you only choose utility spells, you're left severely wanting for attack/defence options, and vice versa. And if you compromise and choose a mix, you're essentially lessening one of the best aspects of being a wizard, that of utility spells. Even if you go against the formula I stated, you're still left in that conundrum of losing out on part of the reason to even choose to play a wizard, or being effective in combat.
And all that isn't even mentioning how your core ability is the dumpstat of this edition. I would argue that this limit should be increased to 3 per level instead of just 2. That mitigates all the above issues while still requiring some reliance on luck or DM fiat.