Okay, title is a little click-baity but question is semi legitimate.
I was having a talk with someone about what's the best Metallica album, where they fell apart, etc. We were talking about stuff they did 'different' over time and how far they got away from the sound of the first albums, etc. One of the things that came up were 'not so metal' tracks, ballads and not explicitly "drum-bass-guitar"-centric songs.
So anyway, thinking of them as a thrash band primarily, I went through the catalog from the beginning to see when you start hearing any of the stuff mentioned above and really any 'not a thrash band' stuff, then realized they always had some weird shit on their albums.
Kill 'Em All: There's six songs over 5 minutes long, and Four Horseman is over 7 minutes long (!). That song in particular definitely has some 'weird' parts and changes in them, including what I used to refer to as the 'Sweet Home Alabama' solo break. Also, Pulling Teeth could be considered a filler track but it's essentially a 4 minute long bass solo; idk, pretty proggy.
Ride the Lightning: Fade to Black comes to mind as definitely NOT a thrash song and maybe even barely a metal song, which also has a bunch of sprawling 'anthem' type parts that aren't just typical 'intro-verse-bridge-chorus-verse-bridge-chorus-solo-chorus out'; it's also almost 7 minutes long. And then obviously Call of Ktulu -- it's a 9 minute long instrumental, more sprawling parts and a good bit of changes.
Master of Puppets: The song Master of Puppets gets REALLY fucking weird after 'MASTER! MASTER! MASTER!' and the entire solo section comes out of nowhere; also the bridge has an odd syncopated feel to it that's more fills than it is beat. Orion doesn't need much of an explanation; 8 and 1/2 minute long instrumental song, more sprawling part-work that goes a lot of places. Intro to Damage, Inc. is more 'not a metal band' sounding, especially coming out of the instrumental track. Three songs on that album over 8 minutes long... pretty proggy.
And Justice For All: The title track is 9 minutes long, and it has an especially long intro with lots of changes before the vocals even come in, including syncopated drum fills and classical guita; then the drum+guitar stuff that seemingly has no time signature at all before they start spamming the main riff. One, another long ballad but probably more metal elements than not. To Live Is To Die -- another instrumental track, tons of unrelated changes and the syncopation/swing gets REALLY heavy about 2 minutes in, then there's the Dream Theater-esque voice over. Four songs over 7 minutes long, two of which are almost 10 minutes long -- hm, seems like prog.
Didn't bother going past that point, since I'd say most people would agree Metallica wasn't a thrash band by the Black Album and they weren't really a 'heavy metal' band by Load either.