Hey! we use metadata all the time that is passed in at time of install and then the Dynatrace cluster processes that data based off of Auto Tag rules. While I cant say how large our footprint is.... i can tell you we have tons of tags and hosts and see no degradation on loads and functions in the UI.
The only slow down we saw was that metadata shows up almost immediately, then the tagging rules can take 5 - 30 mins to apply and populate, but keep in mind we have a very large footprint. Dynatrace is aware of this and is working on faster processing for this. But keep in mind, this is only once that the tags really apply and I tell people that once we install it, give it 30 mins for the tags and the Management zones to be applied.