On top of what AZ stated about the noise (Which is spot on), the carpet also keeps some of the heat off your feet. So, if you are coating the inside of your tub for better protection then hell if you want to put the carpet back in go for it.
Most people line their tub so they don't have to have the carpet, or so they can protect the metal and be able to take a hose to it if they want to. But there aren't any "rules" for this stuff.
I took out my crapy old carpet and decided I wanted to replace it with something other than carpet. I ended up buying a molded rubber mat to fit the tub. Once I cut all the holes in it that I need to make it fit it will be reel nice.
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