Nah, I think you are being very dishonest here. When Oda shows you Nami noticing that heat does work against a snow woman who screams in pain because of it, the message he's conveying is that Monet was hurt by it. Because yes, Monet is screaming in pain: if you check the Japanese version you will notice she's screaming in the exact same way as when she's slashed by both Tashigi and Zoro and bleeds; is she also reacting with surprise when she's cut and bleeding?
On top of this, Monet can be delayed with attacks that don't work on her; hence why Robin breaks her body into pieces in order to stop her for a moment (in a similar fashion to other logia being stopped for a moment). But when Robin tore her apart Monet didn't scream in pain, nor she was quite serious and upset while looking at the hole on her body, nor was it ever stressed that it "does work" (compared to what...?) in quite a reasonable way since she was melting snow with heat, not simply breaking it, in an elemmental interaction that reminds of rubber and electricity or water and sand.
There is zero indication that Monet took any damage from that, so the only one who is dishonest here is you.
There were no bruises, no burn marks, no blood nor any other indications of damage done to her arm...
Arguieng that a character saying "Kyaah", in response to their arm being blown off, has to mean they were injured, is nonsensical.
In this panel where Monet thinks she got cut by Haki and is dead she doesn't say anything... so you don't have a point.
Regardless you would only have a point anyways if literally every character in the series would only ever have screamed when taking damage but i guarantee you if you look through the entire manga there are multiple instances disproven that take.
I don't think this is how logia bodies work. Jozu smashed Kuzan to pieces with haki and he wasn't gone. Rayleigh slashed through Kizaru's light upper body and he wasn't beheaded for it. Both had their real body affected yet the damage done to their elemmental body wasn't comparable to the actual damage their flesh suffered.
First off when Aokiji bled from his mouth that was the indication that he took damage, nothing similar happened to Monet.
2ndly Aokiji's ice form was smashed to pieces as a result of the force created by Jozu's tackle.
Jozu attacked Aokiji with haki on a certain point of the latter's body and only that part of his body that he made contact with was no longer intangible and took damage whereas the rest of Aokiji's body was still intangible ice which again, only broke as a result of the force being used.
Also a wild comparison anyways since Nami's heatball literally worked like an explosion that blew up Monet's arm from inside out, those attacks and what results they would have are not really comparable.
Rayleigh never slashed through Kizaru's whole body lol.
Kizaru dodged the attack in the last moment and therefore Rayleigh only caught his cheek.
Many things wrong here.
1) Zoro didn't cut Monet in half with haki, she didn't even bleed a little bit from that. He simply slashed her snow body and defeated here with sheer fear. No haki involved.
2) Logia users whose elemmental body is utterly destroyed by haki attacks are perfectly capable of regenerating from it; again, check Kuzan versus Jozu and Kizaru versus Rayleigh and Jozu versus Crocodile (only his legs keep their shape) for comparison.
3) It took some panels, but Monet's body did regenerate from Zoro cutting her in half. She then tries to attack him and Tashigi puts her down for good.
4) An intangible body that is slashed without haki may still not disperse around the cut; check Kizaru versus Apoo for comparison.
While I appreciate the effort, I don't trust Oda following real world logic for his counters in such a hard way. So it's pointless to argue from them, he's way more simplistic, hence why Luffy's rubber wasn't melted in front of whatever millions of volts Enel stroke him with.
1. It doesn't matter whether haki was used or not since Monet's body reacted in the same way it would have IF it had actually been attacked with haki.
Monet was unable to put herself together after the attack, even so haki wasn't used, simply because she though and therefore her body reacted AS IF Haki was used.
Whereas she instantly rebuilt her arm against Nami and even further transformed.
2. Depending on the damage, yes Logias can rebuild themselves from damage done by haki.
Has nothing to do with this discussion though cause the damage we are talking about blew up her entire arm.
If Monet's arm would have been blown up with heatball + haki it would have been gone.
No logia user in the series has ever had his whole body or a body part exploded by haki, and it's also never gonna happen cause that would mean instadeath for the logia user.
3. Against Nami she instantly rebuild her arm and transformed.
Against Zoro she was unable to regenerate because her body reacted in a way as if it had been cut in half with haki.
4. Snow and Light are extremely different elements/materials behaving extremely differently under different circumstances... and therefore however they may react to damage being done is not comparable at all.
Oda has followed real world physic laws pretty well so far.
It's a misconception that Luffy should have been burned by the lightning anyways.
Everybody else who was hit by Enel's lightning did in fact get burned by it.