another troupe comes in and uses all your sets and equipment to perform the same
show and profits off all the work you did, while you get zero royalties.
There's some ambiguity in how you're phrasing this.
If you're saying that we do a show at a third party theatre, we build sets and do the show, then the next troupe to come through uses the sets we left behind without reimbursing us? Yes, that would be completely proper. For that matter...let's make it even "worse" and say that the second troupe to come in only even chose to do to same show for the specific reason that there were pre-constructed sets already available for it made by us. That would still be ok.
On the other hand, if two troupes are sharing the same theatre concurrently, say...troupe A performs on Thursdays and Saturdays, and troupe B on Fridays and Sundays. Troupe A builds the set, and Troupe B uses them too. There's the potential for trouble there because Troupe B might accidentally
damage the sets during their performance nights, causing us to be unable to use them on ours. That wouldn't fly. But the metaphor there is not a copyright issue, it's a property destruction issue.
On the other hand, if they see our set design, and
copy it...again, I don't see a problem with that. It would be highly unusual for two different troupes to both be performing the same show concurrently in the first place, and I imagine that would ruffle some feathers, but ultimately that would be up to the the theatre owner, not the performer's companies. If a theatre books two different troupes for the same show at the same theatre...there's likely to be friction over that regardless of set procurement arrangements.
You could probably come up with a better example. This doesn't work well because you're talking about physical objects. But if they use our sets that we built and left behind without reimbursing us...yeah, nobody would have a problem with that. But if they're using finite, limited resources like sets and equipment, that we're still using, and thereby incurring a risk of loss by accidental damage...yeah, that's a problem, but it's a problem that isn't really representative of the point I think you're probably trying to make.
Would you care to clarify?