I feel that it would be very unlikely for a House to have no assignments, but I guess that is what would happen if no one was a fit.

I- just-t send them off to Hufflepuff...-

^ Why Hufflepuff? What if they're not loyal or kind? I think Ravenclaw would be a better option since you basically only have to be smart

Not me half dissing my own house-

They would send them to any house they prefer the most ig or have the most positive feelings towards?