Multiple identifier systems can work in parallel, though we should be 100% sure we can’t reuse an old one if we propose to create a new one.
One problem is likely to be the conflation of identifiers for different things. So institutional identifiers can’t substitute for collection identifiers.
There is also the problem of merging and splitting collections and what happens to the identifiers in these cases.
Ultimately, a big problem is that there is no consistent definition of a natural history collection and it is difficult to image there ever will be. Therefore, we have to rely on collections self-identifying their own collections and describing what they mean by a collection in the metadata of the description.