What you mean is a web app, I was supplying web apps to small business for a few months but changed to native apps a while ago, being in the app store was more prestigious and easier to sell.
I am glad I did because at the moment there are so many issues with iOS7 that my web apps would be unusable.
Unless apple makes changes to mobile safari (no guarantee they will) you won’t be able to add an icon to the device home screen and many functions (app cache, back button, send email, url, sms, alerts etc) will not work. You could run the app in another browser with a bookmark to the app but without a home screen icon it’s all a bit pointless, you might just as well have a mobile enabled website and connect to it with Safari.
Even if the issues with apple gets sorted out you have other problems because Mobione will only host your web app for a limited time (50 days? I can’t remember exactly) you will definitely have to host the apps yourself as you mentioned.
I hosted my web apps successfully but it took a while to get it right. You cannot host a native app yourself but you can host an Android app yourself, only trouble is they wont auto update like they do in Google Play.
I don’t know why people don’t like apple, the distribution process is easy and the apps are so much better.