You'll be shocked how easy it is!
This is one of those things that doesn't really bother me. I've been able to hide the arcade monitor bezel and keep the monitor in tact. It just depends how you do it, and what your comfort level is. My current arcades are a mix of decased and still in their factory cases monitors.
This is my defender with a LCD, clear plexi and the default factory case:
In this case, I used construction paper that I spray painted black and cut into strips. I attached those strips to the monitor case before mounting to the TV. It looks very close to factory.
This is a LCD behind dark plexi. If you plan on using smoked plexi, you really are wasting a lot of time right now for something no one will see.
Galaga cabinet using an arcade monitor and factory bezel behind clear glass. This is perfect authenticity and if the question is if it presents better than the LCD behind clear plexi with construction paper bezel, I'd say the answer is no. No one, including myself, notices.
This is a star wars, using a CRT behind smoked glass. You can't see anything behind the glass until the game is turned on. I used a construction paper bezel, but you are unable to see it. Next time I have access to the controls, I'm going to reduce the brightness of the monitor to reduce the light bleed, but it's nowhere near as obvious when you are playing the game.
To me, if you are going to use clear glass or plexi, you can maybe justify all the work to decase the monitor, but if it's behind smoked plexi or tinted glass, you are doing a lot of work for nothing. I know you definitely aren't afraid of doing a lot of work, but wanted to give you some reasoning for why I think decasing is usually more work than it's worth.
Good luck.