Short answer: Vox is retarded and arrogant, just like every other mf in Pentagram
Long answer: Since all of Hell now knows that angels can get killed with their own Angelic Steel, in no small part due to Vox himself recording & broadcasting the entire Hotel fight right up to Adam's death, he'll probably try to exploit the fuck out of that weakness, and quickly amass a makeshift army of hypnotized Sinners with angel weapons (probably gonna steal some of Carmilla Carmine's stock), then straight up march them to the Pearly Gates. Maybe he thinks Adam & the Exorcists were basically Heaven's strongest fighters for some reason? (Considering that our pivotal characters on the Heaven side will be naive retard Emily, dumb bitch Sera and fat nepobaby Abel, Vox wouldn't be entirely wrong...)