It's a great, well-thought-out list, as some of my favorites are on there: Mario Kart 64, Donkey Kong Country, Super Mario World, and to a lesser extent Sonic 2 (given that I never owned a Sega system in my life) and Super Smash Bros Melee. Also, I didn't read about sports games and their validity in your list, but there are a few of those that I can mention as well, most particularly NBA Jam: Tournament Edition and Tecmo Super Bowl. I haven't played it yet, but I'd agree that SM3DW is the game that seamlessly adds a dimension to the 2D Mario elements (classic, non-timed SMB powerups, enemies, etc.). (That's not a knock on the earlier 3D games like Super Mario 64 or the Super Mario Galaxy games.)
That said, save for the Sonic franchise each of the others have noteworthy entries: Super Mario Bros. 3, Donkey Kong Country 2, Mario Kart 8, Mario Kart 7, Diddy Kong Racing, and heck, even Mario Kart: Double Dash!! has aged pretty well, too. (And yes, my gaming repertoire consists of 90% Nintendo IP and NES/SNES sports games.)
Again, these are my opinions, but a few quick (I hope) thoughts on each of these games mentioned above:
Super Mario Bros. 3: While SMW did bring great new additions to the Mario formula (Yoshi being the foremost) and it's deserving of being one of the best Super Mario Bros titles out there, it seemed to miss something more than the Tanooki and Hammer Bros. suit. I guess it doesn't seem quite as...expansive, I guess? True, you have above ground/underground/water/forest/sky/ghost house/castle levels, but, for example, there are maybe 2 ice (cave) levels and no airship levels. You do have the Star Road and Halloweenization of the game once you beat said challenging levels (and yes, it is a challenge--I hate Tubular with a passion), but there are only 7 main worlds in the game (you fight the last boss right before entering Bowser's castle), which, by and large, don't have many distinct features, and don't seem to have as many levels (averaging 4-5 per world).
Compare that with SMB3, where each world is distinct (grass/desert/water/giant/sky/ice/pipe maze/dark) and largely has its own different mechanic (most of which describe themselves and World 8 is primarily airships/tanks/fortresses), and there are plenty of levels to go around, whether you wanted to play them or not. (The biggest knock on SMB3 as compared to SMW is the lack of a save feature but that's easily fixed by emulators or the SNES port.) You also had different powerups (Raccoon tail, Tanooki/Hammer Bros./frog suit) and could enter a level with them by selecting them on the map screen. That said, this is a debate that can go either way and largely depends on which game you played first.
Donkey Kong Country 2: I love the original Donkey Kong Country (and have played it off and on on a Retro Pi), but similar to my comparison of Super Mario Bros. 3 and Super Mario World, the original seems to lack a level of refinement and expansiveness/scope. Don't get me wrong, it's still one of my favorite games and franchises of all time, the music is on a whole 'nother level compared with its era, I absolutely love the environment and theme of the game (including the reboot of sorts for the ape), and ground-smacking enemies with DK or landing a long roll-air jump with Diddy is still very satisfying. That said, it has its share of collision/platforming bugs (especially when timing/platforming/defeating enemies/finding bonus rooms becomes crucial in the final world or two) and kind of left me wanting another world, maybe two, after defeating King K. Rool.
Enter the second installment, which makes not only finding--and beating--bonus levels required for the 102% 100% completion, but also requires the gathering of hidden DK coins in order to do so, but also has 8 worlds compared to the original's 6--the final of which is unlocked after beating the bonus levels. The soundtrack is also otherworldly for the SNES, and the levels are challenging (especially in the Lost World). The only knock I have against the game is that DK himself is not unlockable (say, after beating King Kaptain K. Rool the first time), as he's kidnapped and it's up to Diddy--and the newly introduced Dixie, whose main mechanic is that she show her decent by helicoptering--to rescue him. (Of course, I do like the switching mechanic in the original SNES DKC games and am bummed that it's been removed from the Wii and Wii U DKC games.) TL;DR I guess my main critisicm of the original DKC was that, while great, it was not refined enough as its sequel.
It seems as though my thoughts are running a little long and it's late, but I'll get back to explaining the rest of the games later on.