That seems very inefficient and friction prone. We have stuff like the nix package manager that can install stuff locally without sudo. It also has other nice features from what I've read. What I'm saying is that we need general purpose distros where you don't need sudo to use them.
I designed such a system which runs with appropriate permissions to a task, is modular, and accomplishes the provisioning via 'job' files submitted to a service endpoint. A user could describe the software they want installed. The SA performs due diligence on vetting software and designs a standard install module then generates a skeleton jobfile and provides it to the requesting user to fill in necessary details and submit. Wash , rinse, repeat.
That's the way its done in general: User makes request, request is approved, action. I was noting that a Linux system does not get in the way of that work flow by being a Linux system. If the box belongs to a company then the company gets to decide what is on it.
If the box belongs to the end user then obviously root rights are in order. However, my wife never gets to use anything requiring root rights on her Arch Linux laptop and does not care and would not know what it is anyway. I keep her laptop functioning effectively by watching disc space and other metrics and regularly patching/updating it for her.
On my university we still had real UNIX servers, no way IT could allow for everyone installing what they felt like.
And the local PCs with Slackware/RedHat would get booted via tftp.