Maybe I've missed the focus of this thread but yeah that's exactly what apple has - iCloud Photo Library (ICPL). It will store as much iCloud storage space as you pay for. I currently have 2TB because these twits are making me duplicate my library in the cloud because I moved Photos for OSX between drives on my iMac.
Theoretically, ICPL can be used on your phone/iOS device and will display thumbnails for your library(not full copy until you select to view it full size). However the implementation is absolutely horrible at least for large libraries. I had to upgrade to paying 20, thankfully now 10 a month, for 2 TB and it just simply does not work. I have tried it on an Air 2, a 6 plus, a 6S plus, a 7 plus, and Ipad pro 12.9. It cannot function with the library as large as mine. The app crashes all the time and can never actually show all the pictures further back. I let it sync for weeks and even well over a month to try to sync up from my existing ICPL in the cloud. Complete fail. Apple support just threw up their hands when I called a few times and said it just is what it is.
It's exponentially embarrassing/pathetic for Apple since for FREE, Google photos does all of what Apple promised and more while doing it flawlessly (granted it's not 100% 1:1 archival but tests have shown negligible differences). Apple even went so far as to copy parts of google photos in its last update.
I've seriously considered dropping ICPL completely but then they lowered price down to $10 so I'm just keeping the status quo for now.