Which is also exactly what the CRT itself is – not all of the electrons pass through the mask. The difference is, that the actual CRT part has a longer field to accelerate the electrons, meaning the hit the mask or cathode with a higher energy leading to higher power x-ray photons. Modern tubes just had shielding so it wasn't a concern, the older ones didn't.

Technically x-rays are always generated when a particle accelerates. That's why you can get them even from a high power cyclotron where the particle has a constant force applied on it. The actual CRT creates higher energy electrons and thus will generate more x-rays than the rectifier, it's calculated simply from the voltage and the overall distance of acceleration. But if the TV had a tube rectifier it's true that that would generate low power x-rays as well.