> it suffers from the same oversight every other web component library (polymer, mdl) suffers from:
> - I can't swipe left/right between the tabs
> - I can't pull the menu out from the left by swiping the entire page right
Most native apps don't do either of those two things either... at least on iOS. I can't speak to how Android apps behave these days.
Maybe these are your favorite interaction modes, but it really has nothing to do with whether X is "up to par with native apps."
I'm certain these things could be implemented. Clearly they weren't considered desirable by the authors of Shoelace.
What really holds HTML5 apps back is the fact that Apple consistently drags their heels on adopting push notifications for web. It only has to be available for apps that have been added to the home screen, so all the users who complain about getting nagged for notifications as they browse the web would still be perfectly happy not to be getting nagged. Without notification support, the number of companies who seriously invest in HTML5 apps (instead of native apps) is nearly zero, which really hinders investment in HTML5 frameworks targeting mobile app development (not frameworks just targeting mobile website development).
Clearly, Apple benefits from pushing app developers into the App Store where they can require those developers to give them a cut of the profits.