Warp core unstable: open the door and talk to the engineer there.
Extra warp speed: open the door and tell the engineer to spice things up
Warp breach; open the door and tell everyone to eject the thing
Warp core down: open the door and tell them to get it running now, or get out and push.
See? No need to tap badges or anything. And all of it is communications blackout proof, crazy computer personality proof, engineers console re route and locked out proof, etc etc. It would allow ensign crusher to run the whole eng division, since 90% of TNG just can't happen anymore.