Long story short, your workstation is overwhelming your server with network connections.
Remember that the NuGet.org not only runs on a massive web farm with dozens of load-balanced servers, but it's a static-file based index that's done mostly with CDN-based files.
Each request you make to ProGet, on the other hand, needs to be authenticated, checked for vulnerabilities, licenses, sent to connectors, etc. And I would be surprised if your server is more powerful than your workstation.
There are some features in ProGet Basic like metadata caching that will help, but ultimately when you scale to more developers you ought to invest in better server hardware and eventually load balancing. See https://blog.inedo.com/proget-free-to-proget-enterprise