Breakers for DC need to open the contact gap MUCH larger for a given voltage than breakers for AC. This is because AC has a zero voltage crossing point (happening 60 or 50 times a second for standard utility power) which enables an arc to collapse and extinguish on it's own.
As an example, some of the 480VAC breakers at work say "48VDC max" on them, though they handle 480VAC.
What determines when the breaker will trip is the current and only the current. Shunt trip type breakers and trip in a millisecond on a transient (if setup for it).
Cheaper breakers use average thermal circuit loading (representing average current through the circuit). If you're trying to protect a controller from damage, this type of breaker (along with slow-blow fuses) will do nothing for you, as the damage to the controller often happens in a few milliseconds, and this type of breaker takes full seconds to blow (also the transient flyback from opening under load is equally likely to destroy the controller, but unless you setup a TVS there is nothing you can really do about that).
Essentially, it takes a breaker physically larger and more expensive than the controller to be useful on an ebike, and then it's still a major damage hazard to the controller when it opens (from the transient spike).
A fast-blow type fuse inline with the battery, as close to the battery as possible is the best level of protection you can get, and it's relatively affordable and compact, and if sized right, it should never blow or need attention for the life of the vehicle.
To size a fuse, take the peak current load you should ever see in normal operation (which really requires operating the device under normal conditions to know, the current claim ratings on a controller are often +-50% of reality), and divide by 0.8 for steady state loads, and 0.65 for loads with inrush.
