starting from my comment on this post and then continuing on to other related thoughts.
As a fencing coach, I work hard to teach hit before the foot lands, because hitting before the other guy does is very important. I file teaching to hit as the foot lands under bad/mistaken fencing. It causes other problems or lockups, too, so I really like drills to disassociate hand/foot synchronization (one blade action per step, briefly, to let them feel what they want to do, two blade actions per step to introduce new timing, and then three blade actions in two steps to really break their head open and put it together in a new way).
More likely culprit is our conscious mind. I read an article that mentioned that our brains will synchronize sound and visual stimuli before we're aware of it- up to 100ms and we will perceive them as simultaneous. So if you are seeing a lunge demonstrated and the timing is close, it's going to read as simultaneous. When students start working on it, I often found it easier to evaluate by not looking at them and instead just listening to the thwack-thump.
I was first taught the drop-step concept as a drop with both legs, "elevator down". This had the effect of usually breaking structure in the person you're attached to, and then chambered the body for a powerful upwards strike (or hook, with a bit of direction). Stick work had the same structure in it, elevator down with a downward stroke, then power back up. That work with the drop as chamber led me to use a front-foot drop as a preparation for a fencing fleche. Fleches work best from a low positition with the body tilted way forward, almost falling, so the legs can rocket the body forward with a mostly straight spine alignment. The interesting part of that is that when you pick up your front foot you have to wait until it hits the ground to start the attack. It feels like it takes forever and is incredibly obvious- I have to fight myself not to start early. but it makes for the most blindingly out of nowhere fleches I've done.
Matt Campbell (forgefighting) taught me a sequence of power hitting he learned from Sayoc Kali. It's basically a series of structural forms that allow you to hit as hard as possible- meaning full body-weight plus driving force from legs plus gravity on the downward shots. They're all the kind of shots that it's hard to practice in a competitive setting, in part because they'll do serious damage regardless of protective gear. They will also damage you if any link in your structure chain is off. The first one he taught (the "Plumber's slap") is a full body hook with a step, hitting with the palm. He warned us beforehand that in almost every class it's taught, someone ends up trying it with power before they're ready and damaging their bicep. And, sure enough, despite careful stretching, minimal force form work for a couple classes, one guy messed up his bicep somethin' fierce.
All these full body effects rely on being able to chain structure solidly all the way through your body- your legs can create the power, but if your elbow lets it go it never gets into your weapon. I've been working with my training partner Basil on his power structure. He's got a lot of athletic training- some good Muay Thai, he can murder a Crossfit workout- but he's never had much of the more flexible or eccentric kinds of movements. So I've been hitting him with the Sonnon stuff- weird crawls, strength and flexibility things, Systema exercises, aikido, silat ground/low work. Getting stronger in positions that are imperfect, yielding and pulling form back to center, collapsing and then restructuring to push back. and then I've found the most useful thing to be the aikiken stuff. The sword with a two-handed grip lets you push and play with structure in ways that are easy to feel.
It's been interesting reconstructing technique. I haven't been attending aikido classes in awhile, but I'll take a step, or a weak seam in his power structure, and then say, okay, there's going to be a takedown there, and there's going to be a sword technique, what are they going to be? It feels good to have my different backgrounds and knowledge coming together in new ways.