Rotovators have the big advantage that they don't have as much force on them as a full space elevator and thus can be constructed without such incredibly strong materials. The big downside is that since they are freestanding objects they only act as momentum storage. As they boost things their orbit decays; if you don't want it destroyed, you have to use it to slow things down also.
At first glance this means they're not of much use until we have extraterrestrial mining to provide mass to be deorbited. However, I got to thinking about this and found myself out of my depth on the math:
The normal scenario presented is that a lesser rocket lifts a payload to the rotovator and the rotovator then hauls that payload to orbit. However, lets try a different approach:
A Falcon 9 upper stage approaches the rotovator but couples late, not getting the maximum benefit. It does not detach its payload, the whole rocket attaches. As the rotovator turns it reaches orbit and the payload is detached from the rocket but the rocket remains attached and continues on up, only detaching at the top when it's going as slow as possible.
The rotovator lifted the rocket + payload for less than its full run and then slowed the rocket without payload as much as possible. Choose the attachment point correctly and the energy balances but I'm not sure about the vectors. Am I missing something or would this provide a basically free boost to any rocket that was in the right place?
(And as a bonus this might make recovery of that upper stage viable.)