Why do you think that web applications are stateless? Shopping carts are not stateless, banking applications are not stateless ... any web site other than purely read-only sites are not stateless. Even read-only sites may have caches, ie. state which can change on each request.
I suspect that we are not quite speaking about the same thing when we use the terms "stateless" and "change tracking". In an attempt to clarify, let s take an example, Room Booking:
User X books a room for a meeting with user Y by entering some data and hitting submit
the system makes some entries in a database
User Y wants to change the time of the meeting, enters some data and hits submit
the system amends the data (and tells user X)
So the room "state" has changed in both cases. Do we need change tracking? I assume that we are talking about in some way keeping a record of who made the changes? An audit trail. The answer to that question is not technical, it s down to the business meaning of the change. Here it s a low value action, probably we don t care. But imagine a different business case, one dealing with payments of millions of pounds. The actual pattern of interaction could be the same User X specifies the payment, user Y changes it. Suddenly we really care about who did what and who said what.
In summary, Web Apps are no different from any other app, the individual interactions may or may not maintain conversational state, but useful web apps (like any other) do change system state. The decision about what to audit is a business decision.