"Host tracking" balance the same way LN node does with regular channel. However, is ecash token really stateless? I doubt host shouldnt ensure accountability. 

notgeld

 good use case for chaumian ecash. Everything you know about HC's stays the same with the difference that the host gives you ecash instead of tracking your balance in a database. You can then exchange this ecash with other HC users or just use them for making payments over the channel without the host knowing about you.

bitcoin

I'm Calle, a Physicist and Programmer who fell in love with Lightning - AMA

calle

Yes, and hosted channels are a *very* good use case for chaumian ecash. Everything you know about HC's stays the same with the difference that the host gives you ecash instead of tracking your balance in a database. You can then exchange this ecash with other HC users or just use them for making payments over the channel without the host knowing about you.