Sounds dreadful. The same interface on mobile and desktop ? That'll be a mess.
Everything in the cloud ? how fast to scroll through your library ?
Slow or lost internet connection ? you're stuffed.
Hmm, not sure I agree with you on those points. For the interface, the idea would be the same paradigm and design language, but optimized for a pointer, not touch. That also allows for greater density, exposing elements and options that are tucked away on phones and, to a lesser extent, iPads. Have you tried LR Mobile on an iPad? It’s very good; IMHO a more efficient, effective program than LR for desktop.
And no, cloud centric design would not slow your library browsing. There’re different possible implementations of that model. The bare minimum simply requires the library—but not photos—to be synced through Adobe’s servers. The next step would be hosting the originals online. But every connected device would still keep a copy of the library, previews of every image, and, depending on storage and preferences, a local cache of recently imported or edited photos, or all of them. Each device can pull non-local originals down as needed. This is, in fact, how Apple Photos handles it, and browsing on that program is faster than on LR.
Regardless, if Adobe does go down the Project Nimbus route, I’d still expect them to leave the option where to store the originals to each user; there’d be no mandatory cloud upload.