Minimum jumps is also not the goal! I'm shocked to see how people agree with this so readily. Let's discuss why "jumps" is not a good descriptor. The A button does more than jump, and you can jump more than one time with a single A press. This title implies that it doesn't matter how many times you press A to swim in underwater sections. If it were about jumps, you also would add 1 to the count whenever A is held to buffer a jump I.E. in the 3rd room of 8-4 (it's also held into the 4th room to buffer a swim). The goal is minimum A presses, and it's a more interesting and defined goal than minimum jumps for these reasons. Millions of people have no trouble understanding what Minimum A Presses means, across the ABC/A Button Challenge in various games. Especially in a game like Super Mario Bros., we don't have to worry about people being lost or confused about what the A button does or what the goal is. That is a very small barrier to entry, in the event that there is someone who doesn't know. Long story short: the goal is minimum A presses, not minimum jumps. That is an inaccurate name and it doesn't take things like swimming or buffered jumps into account. The only other name that may be appropriate for this is simply "A Button Challenge." But that requires more explanation.
While it's true that some levels will be very similar, the FDS has enough differences to make a warpless TAS quite interesting. In my opinion, the most interesting parts of the SMB1 warpless TAS are the many ways that the author skips Mario walking to the castle. The flagpole/castle walk is skipped with bullet bills, koopa shells, and clipping into the ground in various ways.
In the SNES version of Lost Levels, this glitch is still possible, but the game softlocks if Mario never reaches the castle. That means this glitch is not present in the TAS of this version. A TAS of the FDS version would take advantage of this glitch. It's seen in 1-1 of the movie that this thread is about. It can be used in more levels, and it can also be used in the underwater world 9 levels, in a way that isn't seen in the SMB1 Warpless TAS!
There are also other tricks unique to the FDS version. Upside down pipes can be clipped into and then Mario can go "down" them. This results in some very interesting strategies, as it warps Mario to different parts of the stage. There are also certain wall clips that don't work on the SNES version, and various enemies behave differently.
In my opinion, it is a shame that a TAS of the FDS version is often seen as unnecessary because of the SNES version, or seen as something that shouldn't be done, because of the requirements for reaching worlds A-D. The most interesting/entertaining tricks are impossible to use on the SNES version. I think the FDS version is very deserving of a proper TAS and spot on the site!