Suppose there was a country with a mountain or mountain range that is the source of a few major rivers. Would floating messages down the rivers (to settlements or post offices on the river) be an effective, or even plausible, means of transporting information? And if so, how reliable do you think it would be?
It might work if you are not worried about on time delivery.
Whatever falls in a river reaches its end, sooner or later: it can happen that floating objects get trapped in the riverside or between rocks, until something releases them. If the trapped thing happens to be a message, it will mean that the delivery will be delayed.
Also note that most rivers have a seasonal regime: during low flow times transportation will be difficult due to the low water, while during high flow time retrieval might be difficult if not impossible.
Another aspect to keep in mind is that anybody along the river can intercept the communication and tamper with it, so you have to forget about secrecy. Even worse, a malicious person can simply cut out your communication lines by intercepting the passing messages.
Even if the flow of the river is consistent enough, and free of obstacles which could damage, destroy, or trap the message, rivers flow in just one direction.
Effective mail means messages can be delivered in both ways. A mail system where you cannot send messages back is not an efficient mail system.