You've described the Technical Program Manager role at many companies, and its rebranded "agile coach" form. In my experience, this role has a lot of value in companies with extremely large projects which require tons of cross team co-ordination and priority discussion. The sweet spot is a project/program spanning 5 teams or more. Where sitting in each teams planning meeting is a full-time job and if someone doesn't do it then some critical but small component will be de-prioritized and the whole project will be delayed for a year.

Think Rockets, Cars, large hardware projects, large software projects where a dozen teams are required to implement GDPR for their services etc.

When this role is placed in a small team of 8-20 engineers it just adds more status update burden to the team, the engineers can more effectively communicate with each other than through a TPM and so the only role the TPM can fill is "pushing". If one can assume that engineers don't choose to slack off whenever someone isn't looking - then pushing just means extra hours, burnout, and missed dates.