I think there might be some confusion: To clarify, there is only one type of NIC in Azure; there are no variations (eg basic/standard.) A VM may support accelerated networking, but this is independent of the NIC.
Load balancers come in two skus (basic/standard), and this is what you might be confusing the nic type with. Load balancer skus can't be changed after they have been created.
Now, all that being said, it is correct that a VM must always have at least one NIC associated to it. There are a few scenarios that do require recreating a new NIC (eg, if you need to move a VM to a different VNET for example.) In these cases, you need to delete the VM (but not the disk), then you need to re-create the VM with a new NIC using the existing disk. There's a number of examples of how to do this: