It's supposed to be an event that gives a fighting chance for the least powerful faction. If factions that already are powerful could snatch it that would make them even more powerful which probably isn't the intention here.
I agree with the OP that only the original faction ought be able to use it even if that faction is destroyed. Or, at most have it so that, if the original faction gets wiped out the artifact is reallocated to the now-current least powerful faction (which would actually be interesting...). Otherwise you get a huge balance issue.
However, if the implementation of that relic makes you unable to build new xeno labs researching completely different other relics, then that's surely a bug and a bad one. Can you confirm that this is indeed what happens? No possibility of not having the tech or the relic being outside starbase radius or been already grabbed by some other faction's starbase or some other cause?