Tekken 4 was made without any consideration of online play. the reason T6 and above have more input lag is to keep online and offline as close as possible.
Shit, tried to run Tag2 after ages of not playing, hoping it fixed himself. First impression, "Damn this shit is laggy as fuck." 20 minutes later PS3 died. Oh well. Fired up T6 to train Kuma. Little less laggy and what do you know, Kuma's stronger here.
At the end of the day I figured I'll fire up Tekken 4 on PS3 expecting it to be laggy like PS2 games tend to. Fired it up through progressive scan and holy crap! No lag, responsive like razor. Shooting electrics left and right. Game had emulation issues with slowdown on some stages. I can confirm that. Nothing like that now, I tried for hours to make it drop frames. Nada. Literally the only problem is occasional graphic glitch on FMVs. I don't know if it's progressive scan or some stealth emu update but the game runs like butter and it's ridiculous how much more responsive than Tag2/T6. Night and day difference.
Also those million gifs were really not necessary :P