2 reasons:
1. Shuai Chiao may do ground training, but the bread & butter that they're famous for is takedowns. Sanshou is not muay thai, takedowns score.
2. Shuai Chiao is a chinese art and sanshou is a chinese competition format.
You could go compete in a BJJ tournament as a Judoka, but it's probably just easier to find a Judo competition.