I have had this interesting idea for a very long time that I just remembered, so I will share it with you. The idea is as follows:

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A cathode ray tube constructed identically to a normal oscilloscope CRT, but with one key change. Instead of the screen being made of standard soda-lime glass coated with a layer of phosphor, make the screen out of uncoated uranium soda-lime glass. I know that from a glassworking perspective this sounds nearly impossible, so the whole entire tube might have to be made of uranium glass.

This will make a final product that has a completely transparent screen, making the electron gun (and deflection plates if present) visible, while still being able to illuminate the uranium glass screen green with the electron beam.

I think this floating image would look super super cool, and would be a nice demonstration as well. Maybe if using radioactive glass is a concern then terbium glass could be used, which is much more expensive but I hear has similar glowing properties.

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Does this seem possible at all?

Also, making a clear MV lamp out of uranium glass would be pretty cool, but that is unrelated to this idea.

The point of an instrument CRT is not to generate light, but to show well readable visual information. Without reflectrions, without any light spots from other bright object (glowing dathode visible through the clear front screen), or any other distraction.
So an uniform gray screen with a bright green pattern on it does the job,
just brightly lit pattern on transparent glass where the light going in back direction is reflecting from internal surfaces and where the cathode filament glow is visible will not make anything like well readable display.

@Medved
You are absolutely right, it would be very distracting and hard to see nicely. The point of this isn't to have a very readable/practical display, but to show the inner workings of a CRT while still getting to see an image.