Why is the privacy for using watch tower services increased with unpredictable commitment tx ids? In the open channel message in BOLT 02 the following statement is written about the various basepoints. 


  The various _basepoint fields are used to derive unique keys as described in BOLT #3 for each commitment transaction. Varying these keys ensures that the transaction ID of each commitment transaction is unpredictable to an external observer, even if one commitment transaction is seen; this property is very useful for preserving privacy when outsourcing penalty transactions to third parties.


I wonder about the last sentence. Why does this in particular help with the privacy of such services? I thought I increase privacy by using several third party watching services and not only one. In case I use one they would know my entire channel state history anyway. 

One thing that I guessed was that once I know one commitment tx I could calculate all txids for all possible channelstates. But I thought the signatures depend on the amount of the outputs and the txid depend on the signatures.

Do I have a misconception or is the reason for the increased privacy another one that I don't see?
Actually, the BOLT has been designed with very strong privacy properties with regard to watchtowers. You can give all your commitment tx id first halves to one watchtower and it still doesn't learn anything about the second halves, others txs or anything else about the state of the channel (or which channel it is watching at all), as long as the full commitment tx doesn't show up on the blockchain. Once it does, it still cannot learn anything beyond this one commitment state. That's what this is done for and it is rather remarkable IMHO.