You can't /shout /yell or /tell with a trial account (or trade or do any kind of marketplace transaction for that matter), so that's unlikely to be the reason.
Honestly, I think it's just a matter of the backend being so old and fractured that it would be such a large engineering project to rework and unify it that they don't think it's worthwhile. The free trial was a relatively late addition to the game, and it always felt a bit bolted-on. Even now, it's a completely separate account, launcher and download.
Dunno about your server, but bots on Balmung use /say to advertise while being underneath the Limsa aetheryte