As has been mentioned previously... this is in operation in Australia. In NSW, the interest from these bonds helps to fund their equivalent of the PRTB.
If the PRTB were to hold the bonds, and a better service from them was the result then I don't see either landlord or tenant losing as a result.
The issue I would see is that the landlord or tenant may not be able to wait for a month for the deposit to be returned. If a landlord has had damage caused to their property then waiting a month may delay the repairs and affect how quickly the re-let it. Ditto for the tenant, they may need the deposit for a new lease and as often happens the deposit from the previous property is ear marked by tenants as the deposit for their new place.
Of course... as with road tax, the revenue generated is unlikely to be used to improve the resources of the PRTB (it's even possible that the more delays there are, the more attractive it would be to hang onto the deposits that little bit longer).