I email stuff to myself on gmail because I can have thousands of things in there that I can instantly find via powerful search. And I'm fairly confident that 5 years from now they'll still be in there and just as easily discoverable.
While Hopper's UI is certainly better than email attachments in gmail currently are, I suspect Google will rectify that on their side much faster than Hopper will rectify my previously mentioned primary two concerns about the data I'm storing.
As others have already mentioned, seamless integration into email would go a long way toward getting me to use this at all. Augment instead of trying to replace is a much better strategy here.