The only time I've ever received cash compensation from LH was for involuntary downgrade F-J and that was hard cash in an envelope. To be honest, the average F passenger isn't going to be overwhelmed by a Eur200 voucher.
As for F being full, I've flown F about a dozen times over the last year (TATL and Eur-Far East) and F has only been full once (HKG-FRA just before Christmas) so you were doubly unlucky.