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?
Basically what you are saying is why should any airports go out of their way to provide toilets extra benefits to customers who are only there to fly?