No,
it does not "beg" the question (pet peeve). It RAISES the question. It prompts you to ASK the question. Just not begs it.
And that's not a simple question to answer, because "best" and "available" are so fluid. Among the best FAs is Kevin Garnett - still an elite defender, ferocious competitor and beloved teammate. But he's old as dirt, so in the long run he's not best.
Also, who's available depends on how persuasive our GM is and how stupid their GM is.