I clean my toilet brush after every use by filling a mop bucket with half hot water and a few cups of bleach.
I then sit the toilet brush into the bucket of bleach and water and let it sit overnight to keep it clean.
Then I rinse the toilet brush off in the morning with hot water again to keep it clean.
Not everyone cleans their toilet brush like they should because they figure hey it's gonna get dirty again anyway but when you don't clean your toilet brush after cleaning your toilet you leave germs on the toilet brush that can get around in the bathroom.
People can then become infected with those germs if you do not clean the toilet brush and disinfect it.
It takes very little time and effort to clean the toilet brush so you should clean the toilet brush and even rinsing the toilet brush off in the bathtub using some hot water and soap is better than not cleaning the toilet brush at all.