Didn't it? OG Hojo disappeared after his death. Dirge Hojo disappeared after the lightning strike.
I wouldn't take a dead person disappearing from the screen in the original game as much of an indication regarding what happened to their body. Dead guards disappear from the field maps all the time, but I doubt they dissolved.
As far as Dirge goes, his body had been there for presumably a few hours by that point -- however long it took AVALANCHE, Shin-Ra and civilian personnel to evacuate the area anyway. It didn't dissolve in the almost instantaneous fashion Angeal and Genesis copies were shown to.
The lightning may have incinerated Hojo's body, sure, or it could have just been thrown from the platform by the impact or when the platform tilted. Either way, though, that wouldn't have anything to do with the mako he drank.