iternabe I find this video by Dr. Shijun Wang quite enlightening on how to understand slur in regard to phrasing. It also answered my question on why slur is needed when in certain music notes without slur are also played in legato by default.
Thank you, iternabe. That was interesting to see how he counted time by the measure on a fast piece. His talk of shaping, though, was more interesting to me since it's more within my reach as a beginner. I think I naturally do some shaping sometimes, like with a higher note in a song I know. Other than that I'm sure I have been playing the notes mostly evenly. Well, now I'll be thinking more about shaping within a piece.