ES Datei Explorer is more than just a simple file explorer. It offers a bunch of additional features, which explain most of the permissions you've listed. I'm using this app for years already and can assure you: it never abused any of the permissions (especially I never saw it making "phone calls", and yes, I supervise such things).
But for the things you list:
- Storage: What do you thing where your files are, um, stored? All file managers access the "storage". Otherwise they couldn't write there, so you could not copy/move files.
- Phone Calls: This is a Permission Group, not the permission
COST_CALL itself. The only permission from that group which ES File accesses is read phone status and identity. So it can detect whether there is an incoming/outgoing/ongoing call (and see the remote number), as well as check your device's ID (IMSI). Not sure what for the app needs this, though.
- Network Communication: This app can also access the network (feature list: Remote File Manager). So you can e.g. use it to copy files from/to your computer, e.g. using Windows Shares (also known as Samba, SMB, CIFS). A feature I really enjoy quite often. So nothing bad about this!
- System Tools: Again a permission group. Here the app requests: modify system settings, connect and disconnect from Wi-Fi, set wallpaper, install shortcuts, uninstall shortcuts, access Bluetooth settings, prevent phone from sleeping. All mentioned permissions are explainable from the app's feature list, though the "modify system settings* is a little unclear.
- Hardware Controls: Once more a permission group. Only used permission here is control vibration. So no danger from that, either.
So the point is to look behind those "Permission Groups" what permissions are really requested by an app, and cross-check that with its features. If something's unclear: ask, as you did :) "Better save than sorry" is a good attitude!
If you're still concerned, and rather want a more minimalistic solution (as you don't need all those features), there are plenty alternatives. But I personally can warmly recommend you this app, from my own experience: It's easy to use, and never let me down in years. No "permission abuse" either.