With a true inbox/outbox client, the ux you would see is:

if a user uses inbox relays that do spam filtering, their note threads will be clean and contain no bots (because the client ONLY looks at the inbox relay)

But if you view the thread of a user with a public relay as their inbox, it will contain bots and spam

So basically it will make it up to the authors to use an inbox relay that does filtering of their choice, not up to the client.

It would be the client responsibility to respect the rule of only checking inbox relays for replies and only sending replies to the inbox, which in the current state of nostr clients would mean many replies would be missed

Perhaps a utopian idea