Having actually played Doki Doki Panic, while it's the obvious jumping off point, enough stuff changed in the conversion to SMB2 that it's really a profoundly different experience (the original game, notably, does not have a run button, which enables shortcuts and generally changes so much about the flow in SMB2, and the structure was that you had to beat every level as every character, not any character, and it was a lot less friendly with bounces off throws).
But anyway, the real reason we got the SMB2 we got is a combination of 3 things:
- Doki Doki Panic was one of the best games from Nintendo at the time, but it was a licensed game with characters from a TV station's one-off event, and retooling it to something they owned outright made sense even without the west in the picture.
- The Japanese SMB2 is just kind of a bad game.
- The timeline on all of this is SO MUCH WEIRDER than you'd think it is.
In the US, we had the NES, and it was just the NES. A box that came out on October 18, 1985 that you put your big chonky carts in and all these games came out on it in an order, with Super Mario Bros. as the very first game (unless you got one of those test market ones).
In Japan though, there were three real distinct eras. You had the original Famicom era, which launched with Donkey Kong, and Super Mario Bros. was this sort of last hurrah, here's the biggest and most complicated game we can cram onto this thing.
Then you had the FDS, which was meant to breath new life into it with a memory extension and the awesome enhanced storage space of a whole 112 KB! Plus you could save games! This came flying out the door with all these awesome heavy hitters that would not fit on an NES cart- Zelda, Metroid, Castlevania, the bad SMB2, and- then it was kind of just a joke because chip manufacturing costs started coming down like RIGHT when it hit, and the thing was so DoA that in foreign markets they just kinda realized there'd be no point in releasing it. Bunch of early bangers then it kinda became the cheap shovelware/rerelease house... with Doki Doki Panic being one of the better later releases.
And then you had the situation the NES was in from the start where you can just shove more memory and bigger ROMs and batteries right on the cart and so by October 23, 1988 we can released the big fancy amazing Super Mario Bros. 3... 6 days before Sega released the Megadrive (or Genesis to you and me).
So here's Nintendo in the U.S. SMB1 is still freaking amazing and people love it, but it was a 2-year-old game when it launched here. The writing is on the wall that the add-on with the sequel isn't going to last so we're skipping that hardware and just waiting for everything on it to get rereleased on cart before bringing them over, and while we're at it, gotta modernize the original Dragon Quest to use battery saves, get that sucker localized (way too late to impress people). After all that retooling, we're not getting anything out the door until September 88 in the U.S. SMB3 is out. Sega's got a 16-bit competitor out, and even if it takes a while to make it over, the PC-Engine which was a pretty real competitor in Japan is on the way. You don't want to be all weird and skip directly from SMB1 to SMB2, but you sure as hell aren't gonna release what's essentially the hard mode expansion pack to this now 5 year old game that was shackled by restrictions that are hard to get your head around today, with all this new shiny flashy competition with more colors and CD audio and such. Gotta wedge SOMETHING in that slot while we wait another year to bring 3 over, so why not the other real good platformer from the same team?
This is also a very long winded way to explain that SMB2 has a better looking Mario than SMB3. Art wise, 3 came before 2.