This is a common practice, yes. Exact parroting can be tedious but A lot of therapists use mirroring to make sure the client feels heard and understood. it's also helps Both the the T and the client focus on what you're actually, literallly, saying rather than presumptions or interpretations.

Many people find it validating because we often fight to Have or feelings or heard in our daily lives or on top of that people often have difficulty articulating what they do feel.