Yes you do need a toilet brush to keep your toilet clean.
Eventually you're gonna get poop stains on the inside of the toilet bowl especially if you have diarrhea or other large poops.
If you do not brush your toilet with a toilet brush and toilet bowl cleaner then it will get nasty and stinky and eventually mold will also be on the inside of the toilet bowl.
You could put a sponge on a stick and use that for cleaning your toilet but that would be harder than just buying a cheap toilet brush.
Toilet brushes are not that expensive and I recommend you have one.
My toilet gets a good scrubbing every weekend unless it needs cleaned sooner.
You can also use a steam cleaner to clean the toilet bowl with hot steam which also helps disinfect the toilet bowl.
Wash your toilet brush after use as well to prevent bacteria and germs from hanging around and making you and your family sick.