You (as with most of us) probably spend so much time on the web now, shuttling around many many different websites, that you don't notice (or remember) that a large proportion of the myriad of native software, beyond a few well polished examples, exhibits flaws that while different are just as annoying, slow, buggy and otherwise irritating.
Bad websites are just like bad software. There's a chance that my making it easier to create apps there will be an increase in bad ones, but there should be an increase in good ones as well. There has been on the web.
I think a good way or restating your point is that, the better web gets i.e. more advanced frameworks with better testing suites, the harder it is to screw up.
A point I'd like to make:
At the end of the day though, mobile _can_ be fast, but it just doesn't compete with native, yet. When I take a web project after concluding an iOS app, I miss being able to run tests and deploy to my phone or iPad in one place and easily. I miss how formal native code feels over a javascript stack. I hope this changes one day, and I love what Firefox OS is promising, but until then, I will be working with native solutions.
Bad websites are just like bad software. There's a chance that my making it easier to create apps there will be an increase in bad ones, but there should be an increase in good ones as well. There has been on the web.