In my experience, most product teams are not well incentivized to pursue adoption over moving onto the next feature or problem to solve.
Dedicated product growth teams are great for this, and if your organization has one, then it's likely their job to drive product engagement. Product marketing can support this with customer marketing and the right messaging, or in targeting non-engaged users / non-customers.
In cases where there isn't a product growth function / team / person, then I think there is good scope for Product Marketing to step up and drive adoption. Key things that this can include:
- In-product comms / marketing (e.g. targeting users that are a good fit with more info or mini announcements)
- Customer-focussed marketing (e.g. blog posts or emails for customers)
- Training of AM / CS teams
Of course all this requires a mandate for the Product Marketing team to drive adoption, a decent understanding of adoption metrics and some relevant systems / tooling to enable these activities, as described by others.