Many features, including mounts and minions, are only available once you complete a certain part of the story quest. My suggestion is open up the ability to send tells once you've joined a Grand Company, just like Mounts.

Now, I know that this will affect regular players as well, but let's be honest, veteran players on new accounts would already have access to the resources they need. Linkshells, Free Companies, and so on, so communication would not be an issue there. As for new players, there's honestly no reason for a new player to send a tell before level 20. The only reason I can think of sending a tell would be to ask for a FATE grinding group near Aleport, and that only happens when leveling alternate classes. Even then, they still have access to the party finder. If the person is a new player that is playing with friends, then they will likely have a way to communicate with those friends other than just through tells.