There are two main objectives when designing conventional structures: strength and serviceability. We want to make sure structures have sufficient strength under very rare and severe loading to prevent collapse. But we also want to make sure they don't move too much under normal loading. It sounds like using silk would be a challenge to satisfy both objectives in many applications. In order to actually mobilize the tensile strength, it would require huge strains that would be incompatible with conventional materials. Or everything would need to be pretensioned up to some high stress. Likewise, for serviceability it would require either lots of strand under low stress or pretensioned strand.

That's not to say these are insurmountable problems, just something Ive never thought about before.