What you always refer as the "blue screen" is the normal UI of the Atari 800 Emulator. The loading of a file via the "blue screen" is the normal way to load a file with this emulator. It is no exception and it is not difficult or hard to understand. The option to load files with the Dingux-Atari UI is limited, cause the underlying emulator Atari 800 uses different options to load different type of files. There is simply no way to load every filetype with one function, unless you start rewriting big parts of the original emulator.
The Atari 800 Emulator has plenty of options, Zx decided, that the user didn't have to use all of them, if he don't want to, so he integrated his own UI into the Emulator.
But with this limited interface, you can't except to have access to all the options, that are necessary, if you want to emulate a rather complex machine, as an Atari 8-Bit Homecomputer. So Zx left the user the possibility to use only a few options of the emulator with his UI or all the options with the original UI.
What you call Pain in the butt is the exact opposite, it is an emulator, written by someone who tries to make something right for everybody, for you, who only want to have limited access to the functions and for the other people, who are interested in the more complex functions of the machine.
Maybe it would have helped, if you took a look at the excellent Atari800 emulator docs. They explain every function in detail.
And by the way, it isn't necessary to load the 5200 games via the original Atari 800 menu. Every game developed for the 5200 exists in an identical version (except for the controls) for the Atari 400/800/XL/XE range. Just take this version and you can load it up straight with Zx UI. In fact these versions are superior to the 5200 versions, cause the 5200 had analogue controls, that can't be emulated on a digital input device.