Where I have lived, it is traditional to either put in a request of no flowers and mention a charity or else you get the flowers.
When my mother died we suggested a donation to her church in lieu of flowers. Lots of people did that, and a few sent flowers anyway (which was fine too). There must have been 200 people who did something (food, flowers, donation), but no one offered money at all. I think I would have been surprised if someone had offered it.
When a friend of mine in Michigan died, I asked his wife if they had a charity that they would prefer donations go to in lieu of flowers and she just blurted out something like "just send us the money we need it." I know I am not quoting her exactly because it was very natural, and I was not at all offended by what she said. I was so glad that she let me know the situation and made sure when I let others know of his death that perhaps a financial contribution might be appreciated in lieu of flowers.
So now I'm thinking maybe this giving of money to the family may be a regional thing. I'd never heard of it when I lived in AR, TX or CA. It does make sense to help people out in their time of need. Most of my relatives when I was growing up did not have an extra penny so if they had a death the money would have helped.
I know my brother has privately inquired of some family members to see if they needed any help with the funeral expenses - which I thought was very kind of him. He paid for everything when my mother died.