I'm at a small liberal arts college, so take from this what you will.
I am a music minor, who has taken 4 private lessons through my school.
My first lesson was violin (self-taught for 5+ years before). Nice teacher, spent way too much time on breaking my bad habits.

Anyway, I suspect he was just thankful for the money since he seemed to be struggling paying bills with his orchestra gig. I asked him straight out what my grade was a few times throughout the semester, he said I was going to get an A. I got an A
👍
My second teacher was my flute teacher. I've never taken flute, but I do have a LOT of experience with saxophone, so essentially the same fingerings. He was nice, but rambled ALL the time. Told me I was going to get an A, got an A-.
👎 I really hope that no interviewer goes "A
minus? In introductory
flute?"
😕 Doubt it will happen but it's still funny to imagine.
My third teacher was my piano teacher. Very nice, elderly lady. Very professional, but definitely willing to talk and laugh during lessons. I loved that she discussed composers, styles, etc. She really enjoyed my lessons because I had experience (17+ years) and just wanted to expand my skill set and repertoire, so I was pretty open to anything she gave me. Asked her what my grade was, she said A both semesters, and I got an A both semesters. In fact, I asked her to write me a recommendation letter.
😀
So, as you can see, lessons can vary tremendously between professors. They are worth it, I think, if you ask around about who to have before hand. I think they make you look more well rounded and lessons show dedication, because they require at least 30min of practice a day if you want to improve. For advanced classes (like my piano class), I practiced upwards of 2 hours a day, in small chunks of course. I recommend a keyboard with noise cancelling headphones if you do take piano, it makes life SO much easier.