text messaging only when iPhone is on

Because the iPad and Mac are not capable of SMS, since that is handled with the cellular system. You need the phone to be on for the text forwarding to work. As you probably already know, iMessage works, but that is because it uses data. Since the iPad and Mac do not have cellular capability, they are dependent on the phone to receive the messages to forward to those other devices.

No. Text messaging, or SMS, is something handled by a cellular phone. In the past it was only capable of being done on the phone, and some computer programs that would connect directly with a phone via wire.

With the newer iOS and ability with the Mac computers, you have the ability to setup Text Message forwarding with your iPhone to allow you to use SMS as well as iMessage with those other devices. It requires the devices to be linked to the phone as long as they are signed in with the same Apple ID and on the same Wi-Fi network. However, since SMS requires a cellular connection, it will only function if the phone is nearby and powered on.

See the SMS section of this support document for help. Use Continuity to connect your iPhone, iPad, iPod touch, and Mac - Apple Support