Well, there is no saying anywhere that training a Padawan is required before being a Master.
That, and Master does not equal member of the council. A number of Masters are not council member.
Some Masters are quite choicey when it comes to taking a Padawan, while some are less anale about it. Younglings aren't attach to anyone. They are just kids waiting to be chosen as padawan. Oh, and they sizzle well against a red lightsaber.