I don’t believe there’s any way to easily do this as described.
The best option I could think of would be to use a slash command instead of a bot and have an integration that periodically looks at all teams and adds the command to any new teams it finds. Slash commands are team-wide and wouldn’t have to be added to each channel, and that would save from having a “bot has joined the channel” in each channel.
If you did want a bot, it might be possible to do something similar by making it a system admin and having it query all teams and then all channels, but I don’t know if that can get private channels.
Your best bet might be to open a feature request. I know there’s at least one for system wide slash commands that already exists.