As to the point in discussion: yes, it can be extremely annoying at times when companies prompt you to download their app. they have good reasons to do it too.
a) you spend good money to build an app, you want to drive users to the app instead of the site
b) many times , the app can be more functional than the site
c) one of the harder things for companies to do , is to retain user engagement. ex, if you have a firm that delivers stock quotes for users, you want to modify the users behavior to use your firm instead of a yahoo finance, or google. by making the user commit to download your app , in a way you get the users commitment to use your service.
d) you get a piece of users mental space , when you get their phone's screen space.
I personally think, having a small, disappearing toolbar to remind the user an app is available is the best way to go. Since every business with a website, also trying to get a mobile presence, a dual strategy of mobile web and app, seems to be the norm.
p.s I usually upvote the stories that I find interesting enough to comment. I choose not to do it this time.
edit:p.s