I would hate a rushed funeral (three or four days).There is so much happens between a death a funeral.
First there s the shock of the death, if it has been sudden, if long and lingering and almost longed for, there is that feeling of exhaustion, grief, relief that someone is no longer in pain. Then everyone has to be informed. This alopneacan take three or more days. In some families, family coming home for a funeral may need to fly or travel long distances and will need to book, transport, possibly hotels.
Then there is the organisation of the funeral,speaking to the undertaker, considering all the options, liaising with church and/or crematorium, booking a hotel or similar for the wake, or organising it at home.
Funeral in three or four days, horrendous. 10 days - fortnight gives you time to do the above carefully and calmly, while giving those most closely berieved to get used to the idea that the person is dead.
More than that, that does sometimes happen in bad winters is difficult.