I'll go over it one more time before giving up. The battery leads carry the primary current and with brushless motors only a fuse is needed there to cut the battery supply in the event of a short. The low current switch goes on the supply for the BRAIN OF THE CONTROLLER. This is commonly a separate wire on our controllers that connects to Battery positive. This is a very low current connection, often less then 1/10th of a amp, that turns the controller itself on to supply the MCU it's power to switch the power mosfets (solid state switches in the controller connected to the battery mains) on and off in a manner that supplies an alternating current to the 3 phases of the brushless motor. Without this low current supply to the MCU (the brain of the controller), the motor cannot run. That means turning that low current supply off, cuts motor power, period.
If you have a DC brushed motor, then the only way to shut down in every possible failure event that could result in a runaway condition is to cut battery power completely. Brushed motors used to be the norm, and that old school thinking that battery mains need a switch originated. High current switches, contactors, etc are required for brushless motors, but they're expensive and bulky, but thankfully unnecessary for the brushless rigs the overwhelming majority of us have.
While about once a year some try to defend their use of big, unnecessary, failure prone switches on the battery mains using brushless motors, I put them in the same category as people who think it's convenient to remove their battery pack after every use, and break it apart to recharge. I wouldn't even ride an ebike if it was that detail oriented and failure prone. Who wants a hobby called fiddling with ebike batteries? I take due care in making my battery connections correctly about once every 2 years, and that corresponds with the same number of times I would need to use a money wasting, resistance adding, failure prone switch on my battery leads. On that basis my "switch" is either a bolt together connection or a soldered connection of large gauge wires. What do I know though? Despite being one of the heaviest guys on the forum, I've got the only 100mph capable electric bicycle, and in 6 years not a single under $10 switch I've used has ever failed, and the keys for them fit nicely on a regular key ring. Had I fallen for the concept that my switch needed to be on the battery leads, there's not doubt in that time I would have been left stranded by a failed contactor at least once, and had to replace others with failure emminent, wasting hundreds of dollars in the process.
Adopt the KISS principle and do things the simple way. I'd bet most using switches on their battery mains don't even have fuses on them, so guess what will happen a worst case scenario, a short of the battery mains? You got it, the contacts of their switch will weld together in the closed position, while they can only stand there and watch their bike go up in flames. Worse yet some idiot with an iPhone will record the event, and it ends up on the news, hurting the cause like any EV fire made public.