The fluffier the cochins, the less they can do the deed on their own. My old mottled rooster could never get it done......never got any fertile eggs the entire time I owned him...up until one little batch this summer. Just random. But its pretty obvious it was a very heavily mottled hen......which is one of my less fluffy girls.
anyways, yes....if you want to show, you usually need to do AI. If they are fluffy enough to do well at shows, they usually cant do the deed on their own.
If you don't show, trim away......