No, a name to identify each horticultural cross is not necessary nor desired in our taxonomy. Such instances are allowed on occasion, but not wanted. Yes, to maintain consistency, all horticultural (artificial) crosses should not be maintained, although I have a feeling the shedding of these names would cause outcry amongst users, many of whom do not maintain or understand the maintenance of our shared taxonomy. If you wish to change iNat policy and our approach to vascular plant taxonomy, you can send a proposal to staff.
Edit: please keep in mind, each individual deviation from Plants of the World Online must be marked and maintained individually. Every artificial hybrid, if maintained, is a deviation. There is currently a backlog of over 18,000 taxa missing connections to our vascular plant taxonomy, all of which need some form of attention from curators and staff.