As a funeral arranger, I'll give some background on why things can be so slow (in England at least).
Here, funeral homes are often part of a corporate business rather than an independent, so you'll have several funeral homes (FH) being managed by one hub. In my case there are seven FH managed by a hub. Only a few of the FH have their own mortuary/cold facility for the deceased.
We have 2 funeral directors and 7 funeral operatives looking after the 7 FH. These people have to have their time carefully organised as they'll be collecting deceased from hospitals/hospices/homes, collecting paperwork from FH and delivering to crematoriums, cemeteries and the hub, collecting ashes and delivering back to the relevant FH, collecting clothes from a FH and taking to where the deceased is resting, dressing the deceased, placing them in their coffins, taking deceased to a FH for a viewing and on and on. There's so much to be done. These are also the people who dress in uniform and attend the funeral so all the back and forth has to be when they're not on a funeral.
It's not cost effective for each FH to have their own fleet of cars, so the small fleet also has to be carefully scheduled so we can't have three different FH organising funerals at the exact same time as the cars and staff wont be available. The cars have to be cleaned and sanitised between each funeral and flowers loaded.
When organising the funeral we will ask the family if there are any dates they wish to avoid - birthdays/anniversaries/scheduled holidays etc. We have to liaise between churches, crematoria, cemeteries, ministers, celebrants etc, and their availability may clash. Often a family could have an earlier date if they opted for an early or late slot at the crematorium, but inevitably they want the late morning/lunchtime slot to allow for travelling mourners. If the family want an order of service printed this can take days to organise as they're done offsite and have to be finalised a couple of working days before the funeral to get them delivered in time.
There are hundreds of funerals taking place every week, and few crematoria to handle them.
Ultimately it's our job to do everything and make it as stressful as possible-free as possible for the family, but you'd be surprised what is involved and how much running around there is behind the scenes to bring it all together.