Can a designer save rejected logos and sell these to other clients in the future?
As a freelancer you should (hopefully) only give away copyright for final, sold artwork, not for any alternatives and/or unsold proposals. In which case yes, you can sell older, unsold proposals to new clients if the artwork works with their briefing.
If you do logos regularly, you will soon build up an archive of rejected proposals which can definitely be adjusted and re-used for future jobs.
The short answer is yes, you can retread your work unless you have signed over copyright. However, there is a fundamental issue here that you are missing. Maybe you should read this article first before you create another logo. LINK: insights_newscred
It's a reflection on the thinking of Paul Rand (who knew a thing or two about logos). Whilst there may be a start point (like a new font you want to develop) or a vector object(s) that you have worked on before, the whole point is to design something that expresses the individuality of the client rather than chuck a random symbol at them. And in the long run this copy shop approach undermines the designers around you who strive to call this a profession, like an architect or an engineer.
On the same lines its important to have discipline in your development work and to manage your time effectively. Paul Rand generally provided one solution / visual to a client - take it or leave it. The rest of us with a mortgage and who are not a genius by nature can be forgiven for providing variations, but really, you should not be providing more than 5 options to the client and ideally just 3.
I struggle with this too (I run free once I am in the zone) although I have learnt to walk away from the work when its had a good input of time, come back the following day and focus on 3 of the best ideas, drop the rest. It saves a lot of time and effort. Put the other ideas in your notebook, they might trigger something else in future and this is good practice anyway - every designer should keep a journal of some kind, develops the brain / creative tap so that you can turn it on and off more easily.
Hope this opens your experience a little.