If you’re not comfortable with the altitude, you’re PIC... use all available options to make your flight as safe as you desire it to be.
As far as the CFI recommendation, maybe they’re trying to keep your workload down and/or they’re concerned about your ability to divide attention between the radio work and the rest of it? Can’t read minds from here, so dunno...
If I were planning that flight, I’d PLAN to go around to the south, and then start asking for direct from Nashville as soon as I was aloft. If they’re busy, and I can’t talk to them, my plan still works. If they answer I say I’m planning direct and see how that works into their world.
It’s such a short flight, loading the plane and the pre-flight would take longer than going all the way around, especially with any passengers, so not much of an issue either way. If I was really on the ball, the pre-flight including weather check and whatnot from the iPad, would be a few minutes shorter than the flight itself. Barely.
Noting the towers is a good thing, of course... looks like there’s plenty of them. As well as noting “stadiums” there, since there’s some overflight rules for those... just know where you are at all times, and don’t hit them.
Low level flights over yellow colored areas always adds a bit of risk, anyway... “Where to put this thing down if the engine quits...”
I don’t disagree with your assessment, but could see going through there also. Personally I’d like a couple thousand feet of air, AGL, under the airplane over a congested area like that, just for a few more seconds to look for a suitable off airport landing location if needed.
Mostly as a thought exercise for you, if you told me for some weird reason we really really really needed to go straight line from takeoff right across there, there’s always the facility phone number... I’d call em and ask what they can do for us coming off of KJWN. Like maybe you have a mission where you’re trying to shoot some very specific video for the flight sequence, or something oddball like that. Controllers will work with ya, if you absolutely had to do it.
But in general, planning to fly all the way around and then asking for better, seems reasonable. Heck, you get them to answer you, they might vector you all the way around anyway... you never know what’s going on in the airspace.
Maybe there’s some guys who called up and said they need to shoot some video, and the controllers need to keep an open space for them until they pop up!
