What is the point of using a cryptographic sequence number if you're not using it as a nonce?
After reading the draft, I think that the purpose of using a sequence number in place of a nonce is because handling nonce in practical situations is very difficult. We need to keep a directory of the used nonces and then do a search through them. You can maintain a heap for the already seen nonces, but the problem is of storing them.

In the draft it says - "The value used in the sequence number is arbitrary, but two suggestions are the time of the message's creation or a simple message counter". This gives a very clear idea that the way they want sequence numbers to be used in practice is to use them in a strictly increasing fashion so that there is no need to store all the seen values and just the latest one can be stored. 
I also think that using increasing sequence numbers which wrap (start to repeat) around after a decent amount of time would also work because by the time the sequence numbers repeat, the validity of the message will long be expired.