If your inbox relay(s) respect your conditions it's easy to make it look the same in your apps.
Discussion
I suppose I was operating under the assumption it would work like your email inbox. You technically still receive the spam, it's just shuffled away to a corner of the UI that you don't have to look at unless you are looking for a particular email that may have been sent to your spam folder. In the same way, your inbox relays would still store DMs from potential spammers (with maybe an auto-delete after a certain amount of time?) but you just wouldn't see them in your client's UI unless you specifically went looking for them.
That said, you are right that making it a policy that the user's inbox relays enforced entirely would mean that the inbox would look much the same in all clients, NIP-04 vs NIP-17 notwithstanding. The user just wouldn't have an option to browse the potential spam received for possible legitimate communications, since the relay would presumably be rejecting those messages.
Can't really enforce it on the relay level without sharing the ability to decrypt the events, since sender metadata is obscured on nip 17.