Rav David Yosef (Halacha Berurah 7:3) is lenient to not require koach gavra or a kli (however he says that one who is machmir to use a kli should be blessed).
He also mentions (ad. loc.) that it's sufficient to wash each hand once, but it's appropriate to be machmir and wash 3 times alternating. The language that he uses to describe this chumra seems (to me) slightly stronger than the language he uses to describe the chumra of koach gavra.
According to this opinion, this "charade" is not "futile", and seems to be a reasonable middle-ground if you can't be machmir for both. (Finding a kli in a public bathroom is not always easy, so I totally understand not being machmir for both.)
(Note: certain things require you to wash with koach gavra, and 3 times alternating, so what I've written doesn't necessarily apply to anything other than using the bathroom. The halacha I've quoted comes from the siman about the beracha of Asher Yatzar.)