Performance Metrics be on Own Server or Own Server Instance
The issue is mostly because of resource competition. Any tool or method you use to monitor your server will introduce observer overhead. This goes for traces, Extended Events, home grown scripts, or third party monitoring tools.

The goal of putting them on a separate server is to reduce further overhead. 

Monitoring queries write a lot to disk at regular intervals, and often get hit with rollup/aggregation queries to report on metrics, smooth data out, etc.

Those queries are usually big and ugly because those tables don't have a lot of indexes. Lots of indexes to help reporting queries would just slow those big/regular writes down.

Production resources should be solely for production data. It's not just a rule for monitoring tools, but for dev, QA, UAT, or demo databases sitting in prod. They're a potential performance liability that's easy to avoid.