The only issue is that it gets political after the first one. After the first time, you know what everybody else has in their hands and can try to make targeted attacks. Maybe not such an issue in practice.
I do suggest that it only work on players with 5 or more cards in hand.
Suggested rewording: Discard a card. Each other player with 5 or more cards in hand discards a copy of that card (or reveals a hand without it).
• When a single card is discarded, it is implicitly revealed; see Jester.
• You don't have to specify that a discarded card comes "from your hand". That's the default.
• The "…or reveals a hand…" bit should be in parentheses; see Cutpurse, etc.