There's very little reason for good tools to exist right now, when notifications don't, and this seems intentional on Apple's part. Great tooling could definitely exist for HTML5 mobile apps to make it a good experience to build great apps that way... except for the lack of notification support on iOS. Historically, the Google Play Store is so lax about things that there's no reason not to just submit apps there. You don't even have to give Google a 30% cut on a lot of things, if you provide your own payment mechanisms. So, making HTML5 mobile apps for an Android audience has never been that appealing. But, that might be changing soon. On iOS, there have always been a lot of motivating reasons for companies to release apps as HTML5 Mobile Apps, but the lack of notifications just completely stops the idea flat.
For HTML5 mobile websites, a hamburger menu is often an unfortunate reality, but I think having the most frequently used links always clickable at the top of the page is better than stuffing absolutely everything into the hamburger menu. HN does a great job with this.