There is no technicqal reason for using unique IVs in this case. But it does not hurt and looks better in security audits.

Edit: there is also an line of reasoning that you should not needlessly expose cryptographic primitives to "non-random"/"structured" inputs as a defense in depth against attacks on such primitives. But when that matters it simply means that the primitive is broken and should not be used (or at least should not be used in that particular way, eg. TEA as hash function in original Xbox firmware).