I plan to use a wizard in a low magic campaign. The DM told me that magic users are few, so scrolls and spellbooks are very rare. He frankly told me that we might only be able to find one or two scrolls/spellbooks over the course of the campaign.

I understand that a wizard is powerful because their ability to adapt with any situation because they have ever growing known spells. But since this is not the case for my wizard, I fear that I might become a burden to the party because I can only rely on the spells gained via leveling up, but not from copying scrolls and spellbooks.

Is a wizard's power mainly from copying spells acquired outside of standard levelling? Will a wizard who only gains new spells at levelling still be balanced across the other player classes?

The following analysis focuses on spell scrolls in particular, but the same logic applies to spellbooks. In terms of their effect on the number of spells in your spellbook, the two are interchangeable.

In my experience, you won't be a burden

I play a wizard in a game where due to some unfortunate relations with the town militia, my adventuring party and I aren't welcome in town any more. Long story short, me and my DM agreed that since I wouldn't have any access to the components I would need to copy spells into my spellbook in the wilderness, I can't copy over any scrolls into my spellbook for the moment.

I've spent a few levels in this situation (4th to 7th) and it really hasn't been that much of an issue. I feel like I still have plenty of options and never found myself in a situation where I couldn't contribute in some meaningful way.

Granted that's just my personal experience. So let me dive into a few clues in the game's structure that tell us that wizards don't need to get scrolls to be successful.

Even without scrolls, wizards get a huge spell selection.

Wizards start with 6 spells at 1st level, and then gain 2 every level thereafter. Assuming you went pure wizard, by 20th level you will have an absolute minimum of 44 spells in your spellbook that you can prepare from every day. Compare that to other arcane casters: Sorcerers and Warlocks have at most 15 spells known at any given time, Bards have 22 (or 24 if you take the college of lore). And all of those classes start with a fewer number of spells known than you have in your book at 1st level. All of this leads to one conclusion:

By design, wizards have access to more spells than any other arcane class. Only divine spellcasters who can prepare spells off of their entire spell list (clerics, druids, and paladins) can compete in terms of spells available at any given moment.

Spell scrolls are magic items

Magic items, including spell scrolls, are defined in the DMG and the Dungeon Master is given free reign on how much treasure to give out to the party. Under this design, the game has to be balanced in such a way that even without magic items, characters can be successful (since the DM could elect not to give out any magic items at all).

Since spell scrolls are a magic item, and their availability is at the DM's discretion, we can then conclude that the design of the wizard was crafted such that they do not need scrolls to be successful and impactful in the game.

Wizards who only gain spells via levelling are still balanced

I have run for a Wizard and, due to my own inexperience at DMing at the time, very rarely gave out scrolls and never gave out spellbooks. However, the player was also not very experienced and enjoyed roleplaying the Wizard more than caring about spells too much (as an indication of our lack of experience at the time, we didn't realise that they should have at least one damaging cantrip at first; the first damage dealing cantrip was acquired at level 4 after getting fed up of trying to bonk things on the head with a staff).

Generally, this character (even after picking up a damaging cantrip) did not feel underpowered compared to the Sorcerer, and Sorcerers have very few spells but make up for it with Metamagic and such. Even a Wizard that doesn't learn spells outside of levelling a) has more than the other arcane classes, and b) won't have that many spells less than those that learn spells outside of levelling because copying spells into the spellbook is still capped by how much gold they have (since copying spells into your spellbook costs money that scales with spell level).

Hence, in my experience running for a Wizard who did not copy much into their spellbook, they still seemed balanced against a Sorcerer, at least, as well as other, more martial classes (incidentally, these other classes included a Ranger and a Paladin, both of which have limited spellcasting, and the Wizard and Sorcerer still seemed like the main spellcasters compared to these two).