“Supervision” does not mean looking over their shoulders. It also doesn’t mean they have to do things your way. Supervision can mean many things. It could mean chatting with the designer early in a project, so that you are both on the same page regarding the design approach and the nature of the design deliverables. It could mean that you have a basis for being confident that they are applying the right design standards and taking the right things into consideration. That confidence can come from past experiences with the designer, as appears to be the case in your current company.
At the very least, I can’t claim to supervise another person’s work unless that person is aware that they are working under my supervision. That means that they know they can (and should) come to me with any questions they may have, inform me of any issues that arise, and offer me an opportunity to voice an opinion when there are significant choices to be made. If none of those things are needed, then perhaps I won’t see the package until the end. This does not seem to me to be much different than what you are describing.
Most of the projects I have signed and sealed were issued to the client at least twice beforehand, for example at a 50% completion level and a 95% completion level. So I would have had plenty of opportunity to insert my own professional experience into the process long before applying my seal.
Here is where I draw the line: If a project was completely designed by another person, and if I had no knowledge that the project was even underway until it is handed to me for a review/signature/seal, meaning specifically that the person(s) doing the design work had no knowledge of who was eventually going to take responsibility for having supervised the work, then I would call it a violation both of law and of professional ethics for me to agree to sign and seal that package. The most I could do, and the law explicitly allows this, is to perform a review, write a report of the results of my review, and sign and seal that report.