In theory, they can be done just fine without blockchains, but in practice, it doesn't always work out that well, especially when the borrowers don't have much money. Matt Taibbi's recent book
The Divide described all sorts of abuses, in which loans are sold and resold, the loans' owners swear they have records they don't actually have, courts trust them because they don't have the resources to check, and borrowers lose to default judgements because they weren't properly served, and in some cases didn't owe the money in the first place or had already paid it off.
Whereas if the loan and payment data were on a public blockchain (with personal details hashed), records wouldn't get lost and courts could easily verify them.
You could argue that we should reform our centralized systems, but that's hard to actually do, which is sorta the point of removing the need to trust them in the first place.
http://www.blunderingcode.com/ethereum-credit-cards/