June's body was especially broken after the purification. Even if Belledel offered to heal most of him, the angel could only put together what could handle his divine healing. The burns were left out—as well as the hole in his chest; but at the very least, June had his entire body back.
That was why Lucirien was slowly healing the human with what he could. June's flesh could not take on a lot of healing in one snap; neither did Lucirien have enough to heal him just like that. It was a good thing. Moreover, with June injured like this, he would still care about a few things aside from wallowing in sadness and regret.
What happened to Ares was heart-wrenching, but there was little to be done from their side.