@karactr
Personally, I think hand signals or whistles, given the distance, would be more managable.
This is highly dependent on the complexity of the message you want to send and the final distance.
The myth wasn't just sending the message the distance of a single bow shot. It was a relay. So say we are sending the message 1 to 5 miles by relay.
For simple messages, a word or two, maybe even a full sentence, you are probably correct.
Whistles could be good for a fairly long distance, but not miles with something that a human can do without tools and if you are trying to imitate bird calls to conceal that a message is being sent, that will shorten the distance even more.
For hand signs, from what distance do you think complex hand signs can be read reliably through woodlands?
So, we haven't eliminated the relay concept.
On the other hand for a more complex message, say a couple of paragraphs of written text, relay by hand signals or whistles wouldn't work. Even with a complex enough hand signal code (definitely possible) or whistles (maybe) you would run into telephone game problems very quickly. The intended message would become too corrupted too quickly.
For the complex message, what are your other options given the time period? There are only two other options to send the message with any speed, a relay of human runners or a man on a horse.
Man on horse would give the most flexibility in terms of source and destination, as a horse can run faster, farther than any human, and no relay is needed.
On the other hand, if speed is essential, no horse can outrun an arrow.
So manageability comes down to how complex the message is, how far it has to go, and how fast it needs to get where it's going.