Should I remove a stolen iPhone from my Apple ID?

If you remove the iPhone from the list of devices using your Apple ID, you will be doing exactly what the thieves are hoping you will do......remove Activation Lock from the phone so that they can now set up the phone as their own, or sell it as an unlocked device.

Whatever you chose to do, you will never see the phone again anyway, but you can really frustrate the bad guys by not removing the phone from the list of devices using your Apple ID. The phone will remain Activation Locked and useless to them. About all that they can do is sell the phone for parts, making a fraction of what they could make if the phone was unlocked.

No.

Do not remove it from the list. Issue an erase. Removing it just frees up the device so that the thieves can use it for themselves. Otherwise, it's activation locked.

Nothing will be updated on the stolen phone since the bad guys cannot know what new password you are now using.