polarised lenses are fine most of the time apart from as you rightly pointed out reading LCD displays and you might see weird lines on the windscreens of old cars, not modern cars though. They cut light reflected in a horizontal plane, so if you look at a river or shiny surface and lean your head to the side then there is a bit of a weird effect.
The benefit of polarised lenses is in their glare reduction for drivers, though it's rare here, very strong sunlight can cause a road surface to reflect in a peculiar way. I've experienced it in France, stuck my gittish Oakley riding glasses on and BOOMSHANKA! I could no longer see the bizarre mirror image of one car atop another in the distance. Never had that here though.
Cosmetically, Polarised lenses look the same as regular tinted lenses,
are you thinking of lenses with a mirror or to use oakley's terms 'iridium' finish?
Your recommendation of photochromic lenses is not so good as they work poorly behind a car windscreen due the the UV protection of the screen.