It's splitting hairs when it comes to the greatness of The National to me. My only criticism of High Violet may be that it doesn't have a lot of diversity or range. Every song is good, but I think that about pretty much all their albums.
Demons might be the worst song on that album lol. But I Should Live in Salt can get me to shed a tear no matter when or how I'm listening to it. Pink Rabbits is an all-time favorite song, I could play it on repeat. Actually, looking down the track list, this may be the one that actually has a couple duds (Demons, Heavenfaced, and yeah, those two).
If we were to rank the four The National Studio Albums of the 2010's, I'd go:
1. Sleep Well Beast
2. Trouble Will Find Me
3. High Violet - admitting its impact and what it meant for the band
4. I am Easy to Find - the only one of the four toward which I had a mixed reaction, as Matt does not need a bunch of guest vocalists (as Ezra Koenig doesn't, either)
But I'd say your approach to music, the track-based approach probably fits them the best. I think their best albums are Alligator and Boxer. So here are my top ten The National tracks of the 10's, some really persona, some of the popular ones, but I guess they're all personal anyway:
1. Carin at the Liquor Store (SWB)
2. Pink Rabbits (TWFM)
3. I'll Still Destroy You (SWB)
4. Bloodbuzz Ohio (HV)
5. Sea of Love (TWFM)
6. I Should Live in Salt (TWFM)
7. Terrible Love (HV)
8. Born to Beg (SWB)
9. Don't Swallow the Cap (TWFM)
10. Lemonworld (HV)
I could honorably mention some tracks from I Am Easy to Find, maybe Rylan and the title track, but I just never LIVED with it, and I feel like that's what you do with National songs and albums. You play them over and over, car, home, wherever, and I had no interest in that with Easy to Find. It actually just got me listening to Sleep Well Beast more.