The biggest single problem with long-persistence green monitors is that they were extremely vulnerable to burn-in unless you kept the intensity relatively dim. Amber monitors were usually a lot brighter. Computers like the TRS-80 Model I and Commodore PET didn't use long-persistence grayscale... they used picture tubes literally manufactured for use in normal black & white TVs to cut costs.
From what I recall, long-persistence white phosphors existed, and weren't outrageously expensive at the manufacturing level... but they had even bigger problems with burn-in than LP green phosphors did... partly, due to differences in the way people USED long-persistence black & white monitors vs the way they used green or amber. With green and amber, people generally used colored text on a black background. With long-persistence WHITE, people wanted black text on white backgrounds, which caused the monitor to visibly burn in even faster. White backgrounds on 60hz monitors with normal-persistence phosphors were kind of distracting... they didn't necessarily flicker while you were looking straight at them (though they did), but if you tried reading from a book in your lap while using one, you'd REALLY notice the flicker in your peripheral vision. 50hz was even worse... it flickered even if you looked directly at it, and almost felt like a strobe light if you tried reading a book in your lap with the screen visible in your peripheral vision (at least, on a Palbooted American Amiga with a color monitor in a room with 60hz incandescent lights, which might have made the strobing effect worse than it would have appeared to someone in a country where the room lights were flickering at 50hz as well).
From what I recall, green (and probably long-persistence monochrome monitors in general) had TWO intensity controls... a recessed one on the rear (that usually required a screwdriver to turn), and the "official" one near the front. The rear one established the maximum-allowed brightness... the front one allowed users to adjust the brightness between "totally black" and "the limit established by the rear control". In most cases, the maximum-permitted intensity was WAY lower than users would have really preferred, especially in brightly-lit rooms. And despite their relative dimness compared to amber, green monitors STILL ended up with visible burn-in artifacts long before amber monitors of comparable age.
When I was in college (circa 1992), the University had a mix of green, amber, and color monitors in the computer labs. The amber ones were generally less-preferred than the color monitors (unless it came down to, "non-IBM clone with color monitor and mushy keyboard vs IBM VT-102 terminal with silicone-greased clicky-keyboard and amber monitor), but EVERYONE hated the green ones. They were dim, had burn-in artifacts, and just generally weren't nice to use.