…the rules do not mention that Secrets can be played, only that Secrets are not desirable to show to other players or have leave your hand.

A: Secrets, like all cards in Fluxx, can always be played. A state of having nothing left but Secrets in your hand, and still being required to play a card are exactly the kind of situation you hope to avoid.

Of course, if you want to just play them and take the penalty, that’s absolutely your choice. Maybe, to you, the satisfaction of the crime was worth taking the allotted punishment – or maybe you’re just a psychopath who has no shame or remorse about your wrongdoing…