Can there be a category to get all Chao emblems?

On the boards? No.

But by all means run it on your own.

Ok

Opinions differ

Chao casually is tons of fun for people, but a run of it would be extremely boring to watch

I would run something easier. Like getting all Chao levels or something with karate or racing or a certain number of Chao. Also how fun a speedrun is to watch has nothing to do with whether it should be run or not.

The rules should be you must take a shot after every race.