I'd like to see a gap closer similar to Noctis' (FFXV) ability to throw a sword and teleport to where it strikes. Granted, if Gunblade users end up being a thing, this might be more thematically appropriate for them.

Gap closers need not be targeted damage dealing attacks, either. A simple "dash" style move that propels you quickly forward in the direction that you face could be incredibly versatile, especially if it negates knockbacks when activated. Having damage attached to these moves forces you to choose between gaining the damage vs. reserving it for a knockback.

Another variant could be to just give PLD something that significantly boosts movement speed while also negating knockbacks. Give them a pair of angel wings and let them zip around the battlefield casting Holy Spirits without interruption (and make Requiescat ranged, while you're at it).

This is a guess, but I suspect that the reason why you don't see "draw in" effects as gap closers is because unintentional movement seems to sometimes mess up the activation of mob abilities. A classic example in ARR was the use of Holmgang to interrupt otherwise uninterruptible abilities. If you jumped away from the Leviathan Ex mob and used Holmgang while they were casting Dreadwash, the mob would be moved towards you and the spell would interrupt. There was also that silly bug back in Heavensward where people were spinning bosses in a circle quickly, which somehow prevented them from casting abilities. I've always wondered why bosses always "animation lock" when they're trying to cast something, whereas in other games bosses would continue to cleave and throw out attacks while big AoEs were going out.

Gap closing to a player sounds fun in principle, but it only really would work if you also had the option to gap close to an enemy. Part of what makes knockback negation important on tanks is because you want to keep the boss in the same orientation and position. If you could only gap close to an ally, the boss is going to turn. There's also the issue of targeting. Although it might be fun to have a "rescue" themed gap closer where you dash to a location, picking up teammates and carrying them off to your destination as you go. Kind of like the PLD Heavensward Countdown artpiece.