Laura, it's not the idea of cash that makes me twitchy, as MsMary would say, but the idea that the recipient, not the giver, is specifying what gifts are acceptable, and, by the same token, what gifts are not. To my old-fashioned mind, the giver gets to choose the gift. Recipients can suggest (which is the purpose of a registry), but the final decision is always left to the budget and inclination of the giver.
Cash gifts are a long-standing tradition in some cultures, but are usually not tied to a specific outcome. They are generally viewed as a "nest egg" to help the newly wed couple get established. Asking for cash to cover an engagement ring, the wedding gown, the wedding festivities, or a honeymoon seems to imply I'm making a charitable donation. I'm not a guest, but a sponsor, and, as such, I'd like a tax receipt. It's perhaps a fine line, but I'm old-fashioned enough to think that it's one that ought to be respected.
