Given the idea is intended to support more tactical play, making it this simple seems to contradict the goal of the thing.
Maybe I'm just coming at it with too much if a 4e mindset but this mostly seems like a waste of time. Marking groups is difficult at best, and still provides extremely marginal value; there is very little incentive involved, and none at all if only engaged with one opponent (quite a common occurrence in my experience); and the process seems to require just as much tracking as the original.
Further, the "needless complexity" of the original isn't that deep. It's literally just...you need to still be able to take Reactions, even if you don't consume your Reaction to do it. I'm pretty sure you would want to preserve that restriction.
And if we aren't removing that restriction... I'm not sure what your edit is actually changing. Nothing about the Mark action in the 5e DMG says you can only Mark one target. Indeed, this is a significant nerf as well, as you no longer have Advantage on attacks against marked targets.
Overall, I still think this is just an ultimately wrongheaded idea from the very beginning, the original 5e "Mark" action being a stunted, malformed translation of 4e's stuff. You'd be better off just ditching it entirely and trying again from first principles.
Something like
Marked (condition)
A Marked target is being actively tracked by some other combatant, harried or hindered, whether directly with physical objects, indirectly with observation and interference, or at a distance, perhaps using magic or projectile weapons. If a target is Marked by a second combatant, the first Marked condition ends.
While Marked, all attacks made the target suffer a -1 penalty unless they include the source of the Marked condition, and all saving throws for abilities used by the Marked target have their DC reduced by 1 unless the source of the Marked condition is among the targets of that ability.
Then, separately, give various classes and/or feats tools to make use of Marking as a feature, both ways to apply it and ways to exploit it. Presumably Battle Master Fighters should be the preeminent users thereof (probably give some nice hooks for both Fighters in general and BMs specifically), but I could see features for all classes that are primarily about physical combat (Barbarian, Fighter, Monk, maybe Paladin, maybe Ranger, Rogue.)
