You need access to run the app on the local server of your own machine. If the access on your machine is tightly set, then admin access is required. But that’s not a Mendix requirement, but related to your machine config.
In my experience, you need admin rights to install Studio Pro, but then you can run Studio Pro as a regular user.
What admin privileges are you refering to? There is nothing extra required on the latest versions as far as I know. I’m working on Mx 8.9.0 up till mx 8.16.0 without anything extra.