Overview
Whereas the vast majority of CRT televisions had a simple polished faceplate, it was widespread for CRT computer monitors to have a coating on the faceplate intended to reduce reflections/glare, due to the expectation of being used in an office's harsh lighting environment. But there were caveats to this insofar as popular coatings did have trade-offs in the form of decreased brightness as well as sharpness.
One problem which is often resolved at the expense of focus is that of screen reflections. Anti-reflection measures such as silica coating of the face plate are widely used. Although they reduce the problem of reflections, they also substantially reduce image quality. A loss of focus and a slight grey cast over the entire picture are typical disadvantages of such anti-reflection measures. -Dictionary of Monitor Technology, p.22
More advanced coatings were developed that didn't decrease performance to such degree, but they came at a greater financial cost and hence were not universally applied despite having superior results.
As an example, Samsung's 1999 Business and SoHo series of monitors had a silica coating, whereas their Professional series used the more advanced UltraClear coating instead.
If you no longer use your CRT computer monitor in a harsh lighting environment and it has a silica coating, then you can regain lost brightness and clarity by removing the coating. I did this on a MAG 900V and the improvements to brightness and clarity were strikingly noticeable, and made for a much more enjoyable user experience.
Procedure
It is recommended to first remove the picture tube from cabinet, as effectively polishing where the bezel meets the tube may be difficult otherwise (I started polishing with the tube in place but later took it out to finish the job). The materials I used were a power drill, a felt pad attachment, and cerium oxide. The drill was to the lowest speed, a small container of water was used to mix a small amount of cerium oxide powder into, the felt pad was dipped into it periodically, and the faceplate was polished until the silica coating was removed. I didn't clock it but I believe it took less than two hours for a 19" monitor.