Thanks for sharing your feedback and experience Dan. It’s great to hear that you have found working with product teams in a Scrum context helpful. I find it helpful, though, to ensure that the following two conditions are fulfilled:

1. The person in charge of the product, the Scrum product owner, is sufficiently empowered and able to make important product decisions if no consensus within the product team can be achieved.
2. Only the key stakeholders are product team members to avoid that the group grows too big and collaboration and joint decision-making become difficult.

It would be undesirable to have the person in charge of the product act as a proxy, as a go-between powerful stakeholders and the product team. Hope this helps.