Why?

To reiterate, yes you could build a clone, but the odds of duplicating Twitter's success is almost nil at this point.

Or are you asking if they're legally capable of forbidding people from creating other clients?

The tech (multicast messages) isn't patented, and there's no legal prohibition on creating clients. The only client concern is that clients use OAuth, and can be disabled by Twitter staff as necessary. A disabled client is probably legally barred from returning to the service too.

No.