You cash your check for a good percentage of it. If they had a bank account they wouldn't need to spend that money. I don't know how it is in other states but the last time I opened a bank account in California it was a pain. The amount of information needed is certainly not possible for a huge chunk of people.
The dole payment isn't large enough to afford the price of a washing machine - but it is enough to afford the rent for one. Of course in the end you'll wind up paying much more than the outright buy price, but you can't help it, you can't afford to buy the machine.
(Of course these places rent out much more than the "needed" appliances, you can also get fitness equipment, Playstations etc.)
Unless you were in on the ground floor with CPU mining, you aren't getting many coins now. There was only 6 months where you could use GFX cards, and now the "room full of ASICs" take the cake.
Bitcoin is useful if you have goods, services, or currency to convert to it. It is not "free magical money".
Its main attribute is that it is stateless... and that's a big deal and also not a big deal to those whom are in poverty.
BTC highly fluctuates, making storing money in this currency highly unstable. It's good to pay someone across the world, where US banking regs get in the way.
Getting into the BTC ecosystem is hard, unless you have hard currency to trade, or goods/services. Poor people are still at the whim of those whom have.
Cellphones can do that, so while not everyone has a cellphone, anyone that does could create a bitcoin wallet to doesn't charge you an additional fine when your newly opened checking account drops below $50.