What is the possible use of StringWriter and StringReader, which cannot be done by StringBuilder itself?
StringReader and StringWriter derive from TextReader and TextWriter respectively. So what they can do act as a TextReader or TextWriter instance, which string or StringBuilder cannot because they do not derive either of those types.
What is the practical use of them?
They allow you to call APIs that are expecting a TextReader or TextWriter, when what you have/want is a string or StringBuilder.
What could be the possible reason they are not taking up Stream as the input (Because any other writer and reader are taking the stream as the Constructor parameter to operate on) but the StringBuilder?
Because they don’t work on streams; they work on strings or StringBuilders. They’re just simple wrapper classes that adapt these types for APIs expecting a different interface. See: adapter pattern.