R4 cards exploit a security vulnerability that allows the DS to load their menu instead of a game. From the menu, the user can load either games or homebrew from a list of multiple items.
You're correct in saying that SKY3DS behaves like a retail cart. Because of this, the SKY3DS must work within the limitations of actual 3DS games. As such, it can only act as one game at any given time. Pressing the button on the flash cart causes it to write your saves to the SD card and then load up the next ROM in the list, while the 3DS detects it as if the cart had been ejected and then a new one was inserted. The SKY3DS cannot load code of its own, it can only do what retail games do and nothing more. Since retail games aren't programmed to load up a menu and explore ROMs on an SD card, neither can the SKY3DS.
The reason why the SKY3DS can't work like the R4 is because of its entire architecture rather than due to any CPU limitations.