Is it possible to re-insert a LaTeX equation by label?

Usually, almost everything is possible, but what you want does not exist yet (AFAIK). What you are asking for is a macro, which goes back to the label, copies the environment completely and expands it at another place, changing the \label into something like \tag in amsmath.

I'm quite convinced that the hacker fraction here could come up with a solution with less than 20 lines of code within half an hour.

But be warned: Why the amsmath package only offers the \tag-solution? Isn't it more usual to refer to an equation by citing its number than to reprint it completely?

I know this question is old but I thought I'd give my input. It seems like the easiest solution would be to save the equation in a separate file and just \input{} the equation whenever it is needed, using whatever desired means to attach the right equation number to it. Of course this could get messy if you have a lot of equations like this. Maybe then you could save them all in a subdirectory. Not elegant but it should work.