Why do you think blood drives are good? Why wouldn't it be better if the standard thing was to pay for blood? If it was typical to pay donors for this kind of thing (organs too), wouldn't that better ensure plenty of supply than making charity the primary source?
There's a big debate about this, though it's a tangent to this discussion. But it boils down to how adding money into the equation tweaks the incentives of those giving blood or donating organs in a way that's not necessarily good.
One obvious way -- suppose you're filling out a medical history form before providing blood or an organ, and you know that ticking "yes" to a question will disqualify you. You really need the money -- will you be honest?