It would depend on the brand and style of faucet but in general those plates are there for 2 reasons. One is to keep the stems in place as the valve risers are generally smaller in diameter than the hole they are installed in. The other is to keep water splashed on the counter top from traveling down into the cabinet. Some kitchen faucets have been designed to be used with or without bottom plates, but most bathroom faucets have not. As far as your kitchen sink faucet, The plate has simply been incorporated into the spout base, it's still there, it just has been designed to be part of the base of that spout and is the same diameter. For the bathroom plates, A quick wipe with a dry cloth when they get wet can keep those spots away.
Basically, It's all in the manufacturers design. If it is designed so that they are optional, they can be removed. However, removal would entail taking the whole thing apart and reinstalling it.