That's the key difference here. Raw design. The reason not everyone liked the old version is because it wasn't up to its full potential.
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The in-story Naadam was pretty fun, so I'd definitely be up to try a PvP mode. No GCs involved at all, and no alliances. Make it a free-for-all with between three and nine eight-man parties (i.e 24 to 72, the same min/max as Frontlines) all competing for the center. Teams start off a ways from the center and have to run there like in the story version, and there would be some strategy in whether you want to make an all-out break for it and try to end things quickly, or hang back and let the other teams tire themselves out before swooping in to pick them off (If I had my way there would be no respawning at all, or at least a longer wait for it).
If they wanted to get fancy there could be mode-specific abilities or item spawns that you could use to send an enemy back to their spawn point, or punt them to a random corner of the map, since with small teams being even one man down could be serious.
Please read the link I provided for Seal Rock Seize.
Even if they halved the number of fixed nodes (of which the grade and location activation are randomized), and added the Temple Knights, the Doman Liberation Front, the Ala Mihgan Resistance, Sekisegumi, the Confederacy, and the Garlean Empire along with the 3 GCs (an 8 man party for each still adding up to 72) it's still. Basically. Seal. Rock.
I can't stress it enough: The Naadam is a single objective, PvE version of Seal Rock on a different map.