There are different categories of speed runs. They are split up based on how many stars are required before finishing the game.
The relevant categories are:
- 0 stars
- 1 star
- 16 stars
- 70 stars
- 120 stars
There are historical reasons behind each of these categories. 120 stars is effectively equivalent to a 100% run in other games, where you get every available star. 70 stars is equivalent to a fast casual run of the game, since 70 stars are the minimum to beat the game without using glitches.
From there, the other 3 categories exist because people found progressively more effective glitches over time for skipping content. First, someone learned how to skip to the top of the infinite stairs and how to glitch through some doors. You needed 15 stars to open one particularly annoying door, then 1 star to move the entrance to Dire Dire Docks back to reveal the Bowser level, then glitch towards the end of the game.
Much later on, someone found a way to skip through the 15-star door, so you only needed to get a single star in Dire Dire Docks to have access to the Bowser Fight. Finally, someone found a way past even that, so you can just fight Bowser without any stars.
Depending on the category of run you watch, different kinds of content will be skipped. However, none of the runs skip any of the Bowser fights (which is how you acquire keys).
After writing all this and re-reading your question, I have realized I don't know why the key doors specifically aren't skipped. I'll leave this up because the background info might shed some light on the puzzle-solving process of getting this game to the state it is, but I don't actually know why the key doors aren't skippable. Maybe someone just hasn't found a skip yet, or maybe you literally can't start a given Bowser fight unless the previous one has been completed because of the way the game is programmed.