You almost always want the PLM as a responder link for every Insteon device.
This is not necessary for responder only devices such as LampLincs though (if Responder groups does not equal 0 in the types table, you can create Responder links).
Thus none needed for the red boxed device, but suggested for the green boxed devices.
If there are multiple Responder Links, then it is good practice to make this link the first link, so that the PLM will have the greatest chance of being updated.
When you control an Insteon device manually (at the switch), it will send an Insteon Group Broadcast command (unacknowledged without retries) to any device listening.
If the receiving device hears it (the PLM) then we're good. If it isn't heard, then we must rely on a Group Cleanup message.
This message is sent to every device in the Group (in the order that the links appear) up to/until another Insteon message is placed on the power line.
If you have two Insteon switches right next to each other, and first switch one and then immediately the other, you'll get a group broadcast from the first one but the group broadcast from the second one will cut off any (or if you're lucky, the first group cleanup may already be sent) group cleanups being sent and you'll only get them from the second switch (up until another Insteon message is placed on the line).
The second reason its good to have a Responder link to the PLM is that the message is sent directly to the PLM and acknowledged. Due to the way Insteon works, if a Switch controls another Insteon device (but not the PLC/PLM) it will send the group broadcast (which the PLM may hear) and if you're lucky the Group Cleanup message directly to the controlled device (which the PLM may also hear). If the PLM is far away and the switch and its controlled device are close to one another, the PLM may never get a chance to hear the Group Cleanup as the message will stop being repeated as soon as the remote device acknowledges it. (Insteon relies upon a simulcast repeating message network to try and get its messages through to every device).
You typically only need a controller link to a device with the PLM as the controller if you plan on controlling multiple devices through the PLM groups. A special situation would be where a LampLinc (eg, SmartHome Model 2456D2, which can't have a Responder link) is I2CS.
Then you MUST have the PLM address somewhere in its database so a controller link is the most logical answer.