Google does, in fact publish apps that require root access in the play store. Titanium Backup is a popular example (though I'd recommend the open source Neo Backup instead).
They presumably don't publish apps that use exploits to help the user gain root without unlocking the bootloader and wiping the data partition.
Now thats an app I miss using, but unfortunately its much harder to get root on phones now, or if you do a lot of functions like banking apps will not work.
Androids built in app backup functions are woefully incomplete, and switching to a new phone recently I had to relogin to most apps and re-set up nearly everything, except for stuff like contacts and anything from google. At least some apps supported exporting settings to external files and allowed re-importing them.
It's rare I run into an app I want to use that has more than trivial root detection, including my two banks. I would probably change banks before giving up root or mobile banking.
When I do run into apps that are difficult to run, I make sure to give them 1-star reviews. I consider attempts to block rooted devices from running an app to be malware.
There are many file explorer apps ( MiXplorer is my favorite https://play.google.com/store/apps/details?id=com.mixplorer.... ) on Google Play that have optional root access as well. You can use it w/o root, but if you have root it prompts for elevation and then lets you use it.
I also use MiXplorer, and wouldn't be able to read my camera's SD cards on my phone without it because Android doesn't support exfat for some reason. Root is required for it to use its own filesystem drivers of course.
I don't think I knew it was on the Play store. It's a free download from the website, but paid on the Play store. I'd like to make a donation without giving Google a cut - the author deserves to get paid.
They presumably don't publish apps that use exploits to help the user gain root without unlocking the bootloader and wiping the data partition.