Apple supporting PWA (Progressive Web Apps) is hugely important because it enables a future where web apps can natively support browser, Mac/Windows/Linux desktop, and mobile iPhone/Android/Windows native mobile with a single codebase of open technologies.
Why is that important? By fragmenting development effort, the overall product isn't as good on any platform.
There's an app I'm making on the side to keep track of your contacts (like a personal customer management system). This needs to store all your contacts offline, because it'd be too much friction to load everyone you've ever taken notes on over the network every time you open the app.
Right now, the only way for me to accomplish that on iOS is to make a native app. This means I had to learn an entirely new technology stack (React Native and XCode), completely rewrite my views, tie everything into my backend, and go through Apple's Byzantine approval process (which I still haven't done because I can't figure out why my app compiles and runs locally but complains about libraries not being linked when I try to archive it to upload to the app store).
This is unnecessary duplication of work that could've been spent writing new features, makes it harder to add new front-end features in the future (because now they have to be added in two places), and adds a huge lag in the time it takes me to push changes to the iOS client (weeks, vs. the seconds it takes to push a change to the web client).
If apple supported PWA, I would've spent my time making the database keep a local syncing copy on the browser (with minimongo or pouchdb), and then every platform would've benefited from faster page loads and offline syncing.
Until Apple adds PWA support, I can't make as good stuff, and people can't use the better stuff.
When I change my preferred text size through accessibility settings, good native apps respond correctly. If I need voice over support, the operating system knows how to read the view hierarchy to me in a logical way.
When drag-and-drop becomes a thing in iOS 11, native apps will implement that feature well. I think it will take some time for web apps to implement it as nicely (if ever).
There are thousands of tiny details that your web app just won't have. Those details are more important than your familiarity with a tech stack or how long it takes you to deploy something.
You say that:
> By fragmenting development effort, the overall product isn't as good on any platform.
But I would say that:
> By building a web app, the overall product isn't as good on any platform.
I have yet to find a "web app" that I delight in using, though I love many web sites and native apps.
I wonder how much of that is an intrinsic problem with web apps conceptually, or a result of the various limitations and design fuck-ups of the browser vendors.
On iPad it's worse. On iPhone strangely, it's not too bad.