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?