Of the hundreds I have I have yet to carry a coffin. But regularly carry caskets. Even green burials which take place in wicker and reed "boxes" .... They are made in flate panels and then strung together to form a large basket still refered to as a casket.
This is quite literally down my area of operation though... some mayoffer coffins but know it isn't a matter of just cost but sometimes offerings in the local area as well as regulations and customs ... though most of it is very similar there can be quite wildly different processes.
You hope. It isn't the ones who know who you are that push the button. You hope...