While I think it's clear that some of the currently Oyster-only features could be migrated (e.g., you can have a rail discount card on an Oyster card, but clearly it merely requires a way to link an Oyster card to the "account" of the contactless card), others are more challenging, like free travel passes.
I suppose you could just issue EMV-compatible cards where you grant the holder free travel, though I'd expect this would be more complicated than the status-quo (both in terms of needing to register IDs in lists that aren't particularly long currently, and in terms of needing a much larger standard implemented).
The standard exists for this - it's called "Model 3" and is an implementation of Account Based Ticketing.
Essentially your card becomes a reference to an online account. When you tap your EMV card, it uses it as a reference to find your online account and see if you have any travel passes associated with it.
There is talk of introducing it on the London Underground. The system already allows customers to associate a card with an account online to track their journey history. But nothing seems to have moved on much in the last few years.
I suppose you could just issue EMV-compatible cards where you grant the holder free travel, though I'd expect this would be more complicated than the status-quo (both in terms of needing to register IDs in lists that aren't particularly long currently, and in terms of needing a much larger standard implemented).