KeePass2Android is able to open the file directly from cloud services (I use google drive). That significantly improves the experience. I wonder if there is something similar on iOS. It has some other standout features like a custom keyboard and a form-fill service that improve the experience.
That said, password managers are not convenient, so will likely not become mainstream until someone fixes that.
I keep toying with the idea of getting an InputStick, but it seems both a bit expensive and also remarkably large for what it does.