IMHO clearly a distinct feature, related to religion, so no repurposing of kiln or fireplace et al, why not call it a joss paper furnace, and add religion tags? As a key, amenity could cover it, also man_made would be ok, historic would be divisive (assuming there are also recent ones).
Sounds like “toss paper (into the) furnace” but it is still better than
“Automatic teller machine (ATM) for the afterlife, which only accepts deposits, no withdraws permitted (until the afterlife).” (Sounds like a new kind of retirement plan. Wonder if it is tax-deductible?")
I am not very amazed, as this appears to be a Chinese specialty, and generally mapping is not allowed in China so that there are fewer contributions compared to other areas. There are less than a 1000 “religion”=“chinese_folk” of which all but 60 are amenity=place_of_worship, the remaining are cemeteries, landuse=religious or building=temple. There are as far as I can see, no detailed types of religious functions mapped for the chinese folk religion. Maybe so far these furnaces have just been implied by religious landuse or temples?
Understandably, the “fire” in a incense paper furnace, or a crematorium, is different from a fire pit, or kiln. But I can sympathize with the doubt of whether every religion’s devices need a top-level feature.
Besides incense paper furnace, there are incense stick pots, which can be large or small. That’s already another feature? File:PaoAnGongCenser.jpg - Wikimedia Commons
In Japan, there are saisen-bako (coin toss boxes), ema (wooden plates in lieu of actual horses) hanging racks, and omijuki paper tying racks, etc. That’s already at least 5 new features in total.
They should be grouped together eg amenity=religious_offering + religious_offering=incense_paper