A File Manager can ask for root folder access permission but Google will closely control which applications in the Play Store can do so (but if you think that sounds good this is also the same policy they have for SMS access, and Google's enforcement of that has been disastrous as review on the Play Store is a dismal mess).

However, this will no longer get you access to Application's own folders, and so backing things up on Android gets even harder and the OS gets more anti-user.

(To be clear, this should absolutely be behind a Permission barrier. But to block off user access entirely is a toxic and unhelpful move that makes the platform less useful).

Or the One Android App That Does Not Suck: Termux?

Media players are also a big deal for this. I put a lot of audio and sometimes video on my sd card and expect to be able to browse and play it. I am actually doing that right now as I type this.

Sadly it seems that prior restrictions in Android have already taken their toll on Termux: https://news.ycombinator.com/item?id=23224669

Yeah.

So much the worse for Android.