What the privacy measures are doing is giving the user the ability to review requests for access to your personal data by parties you aren't already trusting by virtue of owning the device.
For the most part, apps _do_ ask for permissions, for instance Maps and Safari do ask for access to your location. However, Safari has quite a few UX customizations outside what is generally available so that it asks for permissions on behalf of a website, rather than on behalf of itself.
When possible, Apple will try to create a higher level system so that third parties get access to a better UX (say, a pop-over browser or map control or photo picker) but they are usually slower at doing so.
When possible, Apple will try to create a higher level system to allow third parties to have a better UX here. For example, there is an anonymous advertising API which Apple uses and which they are exposing to apps in iOS 14. This does not result in the 'tracking' privacy prompt.
The largest exception last year was likely Find My, in the face of the crackdown on background location tracking. Since the activation lock/location tracking is part of the system, the UX was drastically different than say Tile's app. Apple launched a third party program for Find My this year as they start to try and make up the differences. They still have a way to go there.