Actually they have asked for F-16, Typhoon, Rafale, and also Gripen (formal request sent to Sweden). Beggars can't be choosers and they will be happy to receive any Western multirole jet. Sweden is considering Ukraine's request to transfer Gripen fighter aircraft - MilitarnyiI think that people have forgotten what are the Ukrainian AF CONOPS and where woud the Gripen / F-16 / F-18 et al., fit into those. The Ukrainians will have a very good idea of what meets their criteria and if they've asked for F-16s then that is what they think best suits their needs. It is in the end what they decide what's best for them and they definitely would've taken rough field operational capabilities into account.
One thing with the second-hand F-16 -- if we look at Europe only the numbers are actually not that great. Turkey and Greece have some but I strongly doubt either of them will give up any. Poland got some quite new F-16s -- so new that I doubt they will ship them to Ukraine. None of the "big" countries in Europe operate F-16. Furthermore most European countries operating old F-16 are already transitioning to F-35 and have sold at least some of their F-16s already. So unless the US is providing a significant number of F-16 to Ukraine, the number of available F-16 is may be lower than some people think...
Norway had around 50-55 operational F-16, but has as already sold 32 to Romania, and up to 12 to Draken International Norge har inngått kontrakt om salg av F-16 jagerfly til Romania - regjeringen.no Norge selger et mindre antall F-16 til Draken International (fma.no)
Edit: the Netherlands was a big operator of F-16, but has lost some over the years and have also sold several: What is going to happen to the F-16s? | Joint Strike Fighter | Netherlands Court of Audit (rekenkamer.nl)