It's "ridiculous" that they don't provide a shower after your economy flight to Singapore? I don't believe showers are a guaranteed minimum benefit of star alliance lounges. Why should SQ go out of it's way to provide extra cost benefits to customers who are not their own premium pax?
How would you advise them to justify it?
Because many of us are regular full-fare economy passengers and are members of KrisFlyer Elite Gold. Because Singapore Airlines is supposed to be a premium carrier. Because many other airlines offer Star Gold passengers access to showers in their lounges.
I have no issue with First and Business being separated form KrisFlyer Gold/Star Gold but to not provide a shower does seem ridiculous for a lounge of a long-haul airline.