After reading your comments and having a short conversation with Gregor, everything's clear to me now. I'll sum up what I just learned so everyone can learn from my mistakes and correct me if I misunderstood:
- While driving at a constant speed, the motors only draw the current needed for them to spin at the angular velocity they already have (e.g. if the wheels spin at 400 RPM and the gearing is 10:1, the motor will only draw the current needed to spin the motor at 4000RPM).
- The time where you need to worry about breakers breaking is during acceleration. You need to design your drive so that when accelerating the motors don't draw too much current for too long.
- Breakers can withstand more current than the current specified on them, but only for a certain amount of time, that can be found on the breakers specksheet.
- Breakers=/=fuses. When a fuse breaks it's permanent and the fuse needs to be replaced, while a breaker will re-set some time after breaking (actually knew that before, but I use the word "fuse" for both out of habit so I'm taking this chance to clarify).
- When designing a drive, don't use a tutorial that's basically for non-drive mechanisms.
If I got any of this wrong, or there's an important point that you think should be mentioned, feel free.
Thanks, Allen and Gregor!