Can Desoldered Solder Be Still Handy?
This sounds like a lot more trouble than it's worth, and probably not even a savings.  Heated solder will have partially oxidized and it's flux will be gone.  I suppose if you melt it the oxidized part will float to the top and you can add your own flux, but unless you are a large commerical operation using lots of solder I really don't see this being worth it.

I am having a hard time imagining how you'd even collect the used solder in a hobby situation.  We have several people here doing electrical engineering and technician work professionally, yet this would make no sense here whatsoever.  Used solder would come drops or tiny balls at a time as the irons are tinned or components desoldered from a thru hole board and the holes cleared.  If I tried to collect the tiny balls of solder, I'd probably scoop up as much dirt and other stuff like clipped leads as I would solder.  A whole role of 60/40 rosin core solder may take a year or more to go thru, so even if all of it could be reclaimed it would be a tiny savings.  Just the wasted time dealing with reclaiming solder wouldn't be worth it.  And then there are the questions about the resulting quality and the extra energy required to melt it down.  No thanks.

Even if you could do all this successfully and somehow profitably, then how would you use the solder?  At best you have a small molten pool in a solder pot.  That's very different from wire solder with flux core.  For the ordinary hobbyist or small scale user, a pool of molten solder is not much use.  We don't have a solder pot here, for example.  I'd get one if there was a good reason for it, but so far that hasn't come up.

Frankly, this sounds like a really silly idea for small guys like hobbyists and even us.