Risa

From the perspective of someone just wanting an awesome time, I agree completely. Or from the perspective of a Star Wars fan who wants all the lore and extended material. And personally, I would never want to skip it, myself.

But the goal of the Machete cut is to take a look at the Original Trilogy and ask: how can we get the best narrative experience out of this? It's ultimately about telling Luke Skywalker's story, and providing context to enhance the experience of his narrative. You put 2 and 3 after 4 and 5 to avoid spoiling the reveal at the end of Empire. You use the extended 2-movie flashback as a way to explain who that ghost that appears at the end of 6 is, as well as to enhance the parallels between Luke's and Anakin's characters; namely Luke's use of force choke on Jabba's guards, and him telling Jabba "you underestimate my power"—the same line Anakin uses on Obi Wan in Revenge.

Essentially, we see Anakin's story as a way to provide further context to Luke's. Phantom doesn't aid this at all. Neither Qui-Gon nor Maul appear in any later core film. Phantom only provides further context to Anakin's story, without aiding in Luke's. In the words of the Machete order's original creator:

Some people claim that Episode I isn’t that bad, and shouldn’t be removed (again, it’s not that it’s bad, it’s that it’s not relevant to Luke’s journey in the way that Episode II and III are). Lots of people like the pod race or Darth Maul or Qui-Gon or they were born in 1992. Whatever your reason, if you want to watch Episode I I’d recommend doing so separately, sort of like an “Anthology” film. After all, Machete Order doesn’t interfere with canon, everything is canonically compatible with Episode I (or any later ones) because we’re not watching fan edits.

The original creation came along with a lengthy essay explaining why, pointing to some possible disadvantages, and addressing those. It then briefly went over their experience trying it with someone new to the franchise. Even if, like me, you actually ultimately disagree with the idea of Machete order, it is well worth the read, because the logic behind it is very well put together. Here's a link.

(Incidentally, I always thought the name machete order came from how you're chopping up the timeline. In fact, it's because the former name of the author's blog was "Absolutely No Machete Juggling".)

I've spent most of the ~45 minutes since writing that last comment reading the machete order creator's update post and the comments underneath it. And I just really wanted to highlight one particularly excellent comment from a user going by "amusingmurff".

I didn't know the "right" way was to skip TPM, and while I find a lot of your points valid for skipping it, I find it to be helpful to demonstrate how the Jedi Order failed. There are references to the Jedi prohibition against strong emotion in II and III, but it is in terms of how Anakin is failing to be a "proper" Jedi by his inability to let go of his emotions and attachments. Ep I shows that perhaps it is the Jedi Council, who only say "don't feel anything, that way leads to the Dark Side!" that are mistaken. Is Anakin's inability to let go of emotion/attachment at the core of his Fall? Yeah. But Luke succeeds in VI because he also fails to let go of attachment and sentiment - Vader is only redeemed and defeats Palapatine because Luke can't let go of the affection he has for a family tie and the idea that his father still has some good. [...] I find it a more compelling story if you see that it's not really a tale of the beleaguered good guys (Jedi) who are outwitted by the evil, all powerful Emperor, but that they contributed to their own downfall and doomed the rest of the galaxy. That way, the OT heroes have to not only do away with the Empire, but probably do away with a lot of the forms of the old order, including the Jedi Code as it was

There's some other good discussion in those comments, including a reply to that one, and I definitely recommend reading through it if this line of discussion is interesting to you.

And pod racing!