The rationale for the design change was to reduce effort/screen taps required to access and edit images storage on your device. The previous design required users discover a tiny blue import button. Manually importing an image and editing used to take many taps, and now it's just one or two. Our Product Manager for Lightroom Mobile elaborates on this a bit more on this and other app updates at this recent blog post: -photoshop-lightroom-speeds-up-editing-mobile-shar...
Accessing the album tree from anywhere is the only advantage, but that is diminished by having to scroll through one page of the useless "lightroom albums" everytime before I can see my useful "my ablums" structure. While the old "starting page" had them in view right from the start. And using the back button to get there was more intuitive.