It is more likely that melting teeth is a reference to cremation. Japan has a %99.9 cremation rate, and it's been that high for over a decade. By virtue of their being an island nation and needing much of that limited land for agriculture, they don't have the real estate for expansive graveyards like the US does.
Cremated remains are often buried, and in Japan there are family graves/memorials where multiple members of the family might have their cremains interred. This is likely what Akira and Ami visit.
A few other points that make it unlike Sekai died in a fire bad enough to melt her teeth:
1) You have to still be alive to have your organs harvested, and it's heavily implied that Kaori recieved an organ transplant from Sekai (she calls herself a bag of spare parts and is briefly possessed by Sekai). If you're in a fire bad enough to melt your teeth, you are not going to survive that long enough to donate your organs.
2) Akira mentions holding her after the accident, which would be impossible if she were just a pile of ash (the teeth are the last thing to burn because of their high melting point relative to the rest of their body)
3) Some early happy scenes have an audio track of life-support noises. Who's on life support, and why would their being on life-support be in Akira's trauma space? The only people he cares that much about are Sekai, Ami, and Maya. Which of those three would have most likely been on life support? The one who dies (neither Ami nor Maya have indicated past medical trauma)
The most likely scenario is that Nozomu dies on the spot, Sekai is left in a near-death vegitative state, and Akira has to make the call to pull the plug and donate her organs as he's the next of kin. And Kaori is the life he saved with that decision -- which is why Selebus mentions that she's one of the most important characters in the game. She's the consequence of the worst choice he ever had to make in his life.
Also, the line "O world, in our dying moments please tell me. Why him?" is written by Akira. Akira is dying on the inside while Sekai is dying physically, and lamenting that it was his brother that dies by her side and not himself.
Finally -- symbolically, the casket used to cremate someone can be viewed as a vehicle carrying the deceased towards a final destination, and poets have this pesky tendency to be really big on symbolism, so interpreting a lot of what Akira says literally is a bit of a trap -- especially when he's in shoegaze word soup mode.
Edited to add point 3 and the following paragraph, as I remembered them after hitting Send.
