What a ridiculous, anti-security point of view. There is absolutely no reason my files should live in the cloud. They are my personal files and I will keep them off the cloud thank you very much. A better iOS file browser would be more than welcome.
As you are the kind of person who trusts Microsoft with access to your files, and to run his or her life on Office 365, so your credibility is shot out of the gate.
Please point me to your evidence that I should not trust Microsoft with my files. (And, for the record, it's my employer who chose Office 365... not me... I use Google, Apple, and Smugmug for most of my personal stuff even though the Microsoft cloud services are very well done). Do you have any evidence, or is this just fear, uncertainty, and doubt?
In my 25 years of IT experience I have seen many people lose important data because they didn't have a solid backup routine. Even people who know they should have more than one copy of a file often don't. Sometimes they overwrite files by accident to a storage medium that has no version control. Sometimes they don't do the occasional file verification to detect corruption, and they discover too late that data is corrupted on their primary drive as well as on all the backups. Local hard drives and network shares are also more susceptible to cryptolockers than files stored in the cloud. Of course if you know what you are doing, and you are disciplined about it, local storage can be very safe as long as you keep offsite backups on portable storage media (and you know how to monitor backup processes for signs of data corruption).
Most reputable cloud services, whether provided by Apple, Google, Microsoft, etc., are more secure than you give them credit for being. Privacy can vary depending on the ToS agreement. Paid cloud services are typically going offer more privacy assurances than free services. Office 365 for Business is FERPA and HIPAA compliant file storage that can capture sensitive data types and block them from being sent via email or uploaded to unapproved cloud locations. Of course much depends on having multifactor authentication enabled. That doesn't mean you store everything in the cloud. From a security and privacy perspective, data is handled and stored depending on the classification of that data. When it comes to personal files, most of us are not storing a lot of sensitive data on our personal devices. Perhaps a few documents that have personally identifiable information that can easily be encrypted and/or backed up by other means. Passwords should always be stored in an encrypted file, encrypted app, or (gasp) even cloud-based password management solution.
Most bad actors don't want your files anyway. They honestly don't care about your files or your computer unless they are trying to extort you with a cryptolocker or other malware. They do want your email. They can use your email to send out phishing attacks, and they can download a copy of your entire mailbox so they can search the contents at their leisure.... looking to see if they can find anything useful that will help them access your financial accounts. They might search your online file storage as well, but they know from experience that most people keep things in their email that they should not... and their online file storage will just be a bunch of photos, videos, and worthless text.
You are of course free to keep your files wherever you see fit. If you prefer to forgo the convenience of cloud storage because you don't trust Apple, Microsoft, etc. you are totally within your right. I have helped a lot of people who lost important data or cherished memories that they would still have if only they had used cloud storage... so if you are going to manage your files yourself: Make sure you do it right and with multiple points of redundancy.
Back to the topic of this thread: File browsing in iOS. There have been some improvements to the Files app, but the real issue here is that file storage on iOS is kind of an afterthought. iOS is an app driven platform where the actual data is often hidden behind the app itself unless it gives you a way to export it. The apps that do create files (photos, text, video, etc.) might use local storage, popular cloud services, or both.
Before iCloud it was not unusual for people to lose their cherished photos because they didn't backup their phones using iTunes. My staff still occasionally help people who have never set up iCloud and have no idea that they should be backing up their phones. Occasionally they will help someone discover a backup they didn't realize they had... they sign into Google and discover that their phone had at least been syncing through the Google photos app. These are all on personal devices. For business devices we default the save locations to Office 365.