tube's high voltage can be dangerous, also the implosion of the vacuum tube can be dangerous, for what little copper you may recover they are best not messed with, if you do learn the dangers from these.
They are worth $3-5 each once sorted. It does not take long. 5 minutes with the proper tools. I find an axe to be brilliant on these. The shock value is over rated. I have worked with these a long time and have used them as high voltage power supplies. Once unplugged the charge dissipates within about 10 seconds. If you are paranoid get a cheap electronic voltage beeper and touch the red wire leading from the suction cup. Cut it first after testing.
Then you have to sort out what to do with the tubes. Some places it is illegal to throw them away etc. Here they charge you for them. Don't break the tubes while removing everything.
The faceplate glass, depending on the monitor has lead in the glass, that can be over 20%. It's very similar to Lead Crystal that ornaments are carved out of.
In our State, the Environmental authorities impose severe penalties on anyone caught processing monitors improperly. The glass is considered Hazardous Waste.
Some day, I'm going to build a fallout shelter and use Monitor faceplates for windows. They were designed to stop radiation from exiting the CRT.