I'm not too aware of how cards are in the US but generally in Europe & Australia (afaik) they're this way. Do cheque cards have mastercard/visa on them in the US (What about maestro/electron)?
You are right -- if the card is bank-issued, then they can simply place a hold and release it without money flowing. With Privacy, it would seem they will need to actually pull the cash to be able to ensure that its there when the final charge comes through. Curious to see how this plays out.
My company used to send us on work related trips which were paid for in advance, but relied on us to provide our own cards at the hotels for incidentals. After a few (presumably less financially stable) employees used debit cards with low balances to check into hotels (effectively leaving them with no money during their stay), this policy changed so now the company credit card is used for hotel check-ins.
I personally hate the new policy because I have good credit and like getting room service, and for some reason I find it kind of emasculating that I'm not allowed to use my own card.
In fact a few places accept debit cards but do not accept credit cards as fees with debit cards can be lower.
There's just a handful of subscription merchants that don't take prepaid debit cards.