On the silly comment about airport bathrooms, that's not even worth answering.
SQ *does* have a business class lounge with showers -- for their business class passengers. They are meeting the international premium carrier standard in that respect.
*You* are unhappy because you do not get showers as an economy class passenger. Let's just be clear about that?
I don't think economy class, regardless of Star Gold or not, are guaranteed or even expected to have shower facilities. I would hazard to say that a significant number of Star Gold lounges do not have them.