MGS3's story works fine on its own, I actually think it's great. That's why I said in my previous post that I wish he had just left it alone.
The problem ended up not being mgs3's story though, it's that mgs4 ended the series story abruptly in incredibly convoluted ways that Kojima ended up retroactively fixing later with PW and V. The Act 3 and Epilogue story beats of MGS4 were a mess because suddenly characters were catapulted from support crew to primary villains with no explanation, and the Nanomachines explanations for everything felt unsatisfying. (Now that we have the evolutionary track of the Parasites into Cipher's Nanomachines, things end up having a more interesting technological advancement arc)
One thing PW and V do accomplish is they make the narrative arcs for the patriots much more natural if you play 4 after V. Sigint's/DARPA Chief's role in 1 and 4 is hinted at in V in a way that feels like a solid middle beat, as is Paramedic's/Clark's, Zero actually has a good deal of development as a character around the main story in a way that would have left the graveyard scene from 4 as a mind blowing reveal had guns of the patriots been kojima's last game, instead of this.
The Boss AI and Paz's revelations about Cipher from PW, if you were going 1 2 3 PW V 4, would come off as big moments of "Why is cipher doing AI research?" (It isn't until 4 that we find out that the patriots are an AI run by proxies) Additionally, the plot thread of the XOF unit shows how dangerous the proxies can actually be. Big Boss himself, with the Truth mission retconing of the MSX games, has a somewhat natural progression into his graveyard scene in 4.
Some of what happens with Ocelot in V also makes the revelations about him in 4 much more believable in the grand scheme of things. He was ALWAYS on Big Boss's side, and he was a master of hypnosis. It also creates an interesting scenario where the Mantis cameo at the end of act 5 would feel like slightly less of a joke in the grand arc of the series, since he was such a big impact on V with Eli. Moving 4 also makes the progression of the themes work too, and the revelations about certain mystical aspects (Vamp) not feel like a nano-machines cop out, because the knowledge about the parasites from V would contextualize that as a technological duplication of a natural force that is near magic in the first place. What V manages to accomplish is FIX Metal Gear Solid 4, and that's a remarkable feat in and of itself!
The proper order of the games is like the Machette cut of star wars. You play the first 2 games, then the prequel trilogy, then both of them conclude in the end of timeline installment. The graveyard scene is the end of Big Boss's character arc. Gameplay and graphics-wise, this also creates a more natural progression for new players. They go from the simple PS1 game to the growing more complex ps2 games, then pw (which is a step up graphically in HD collection from 3), the comic cutscenes call back to the comic codec calls from 1, and the gameplay is more rudamentary than V and 4, so it ends up being a bridge between the old style gameplay and the new style gameplay.
V is a nextgen realisation of PW's concepts, and then 4 is retroactively a streamlining of V's concepts, with an old solid snake being mixed in to the new gameplay style. MGS4 has more complex combat mechanics than V does, while having a more streamlined component to mother base's GMP and development mechanics in the form of Drebin Points and the War Economy. Plus, you get to close out the series with David Hayter and Christopher Randolf riding off into the sunset, which is more satisfying than closing out on MGSV's incomplete ending.
I really feel like where we are now, this should be the ultimate form of replaying the series going forward. 1 2 3 PW V 4. It makes for a more coherent narrative than the mess that was 4 in its day, and has a solid technological and gameplay evolution to play through, which is key to playing the original 3 games in release order in the first place.
(The only downside is that we're left without the full stories of Kingdom of Flies and Area 51 (MGS:Rising's original story) being told. There's also an implication that Kojima was planning to set a game in 1994, one year before the outer heaven uprising, that we never got to. (possibly a game about The Boss set in WW2 or earlier, or another Revengence game, or a Gray Fox game...) Maybe this is the path the remnants of the studio might take in the future, but we don't really know for sure, and there's not much reason to hope that they end up able to develop a full game without their core staff in the future...)