IMHO, American funeral breakfasts have evolved weirdly.

Once upon a time, mourners would gather at the home of the family of the deceased. Everyone would bring food. It was a great tradition.
In our busy, modern lives, we evolved to have wakes in funeral homes (where you didn't have to worry about cleaning your house, etc., especially since you were squeezing in family members coming from out-of-town). People often still drop off food so the family can have healthy meals without having to worry about cooking. BUT, with the need to have a final gathering where everyone can relax informally and spend time sharing memories of the loved one after the funeral, funeral breakfasts have emerged.
Something about the funeral breakfast doesn't set right with me. Your loved one is gone, now you are expected to pay to feed everyone you ever knew. I feel like I'd like to pay for my meal or even some of the funeral expenses, but putting money in a sympathy card feels so tacky (I'm sorry for your immeasurable loss, here's $50?).
I have seen some churches sponsor funeral breakfasts. Parish volunteers do all the cooking, serving and clean up. I would guess the costs are very small. Hopefully, everyone in the parish would eventually act as a volunteer and this would add to a greater sense of community. I think this makes sense. That being said, when the time comes, I'm sure I'll be hosting funeral breakfasts at restaurants where it is so much easier and more convenient (since I don't belong to such a church) and I won't want people sticking money in sympathy cards. But, as a guest, I'll always feel it's just weird.