This is precisely the conclusion Google reached and has used as they work on QUIC.
Even protocol state (equivalents of TCP FIN/SYN/etc) is encrypted, to ensure that middleboxes don't get ideas about what the protocol is 'supposed' to do - ideas which make it hard to change the protocol in the future.
>>Daniel+(OP)
It is really sad that one reason why QUIC encrypts protocol states is to prevent excessively eager middleboxes from meddling with the traffic.