It doesn't actually enable these, since it leaves the monk on 1 hp, so any continuous damage effect will quickly burn through all the monk's ki.
No it won't, at least not usually. Hazards like Lava ususally do "damage per your turn" If the Lava he is "swimming" in causes 500hps damage on his turn he can swm in it for 11 rounds if he has 11 ki and starts with 1hp..
Sure if the goal is to get to the other side there are other ways to do it, but if the goal is to go into the lava there are not many better ways.
MINOR SPOILER AHEAD:
As an aside when i played Princes of the Apocolyse my character (a Sorcerer-Warlock) cast Primordial Ward and dove into Lava (using his reaction to be immune to fire damage). He did this to avoid being attacked.
In that particular adventure the Lava caused 6d10 damage the first time you enter the lava on a turn or end your turn there. So getting back to the original question, as long as he did not go in and out of the lava repeatedly it would cause 66 damage on the first round (33 when entering and 33 on the end of his turn), then it would cause 33 per round after that and 1ki per round to stay there after he lost all of hit points.
Also, a point of physics - molten rock still has the density of rock. You can't swim in it, even if the heat cannot harm you, since you can't sink. Archimedes' principle applies.
You don't sink in water either, yopu float, but you can certainly swim downward in water.
Also, the doomed people in Pompey were found on the bottom of the dried pyroclastic flow, not on the top of it.