If a user is searching for a product and they click on the link to that product in an ecommerce store, they want a product page not your app.
Wikipedia has a horrifyingly bad iOS site, but it's the only mobile site I return to; but there's no other site on the Internet that can do that.
I don't know, but it surely pre-dates the smartphone age when the installed browser wasn't able to cope with a more or less fully featured website.
Is what iOS gets different than what Android gets, "http://en.m.wikipedia.org/..."?
On Android phone with Firefox, at least, that site seems almost perfect: all extraneous cruft removed, important sidebars intelligently incorporated, the main article text provided in nice readable reflowed form, and all other sections expandable but closed by default. It's easy to read and quick to navigate. I can't think offhand of anything I'd change about it.
It's not about defining what experience people get, it's that as they are coming into your site, they get the right experience for your content on their device, regardless of whether they were given a desktop link on a mobile device or visa versa.
As demonstrated in the diagram, this is punishing people who strip the tails off incoming links so the link example.org/stories/good-news-everyone gets directed to m.example.org and the user is left with the mobile experience, but the wrong content.
If it's an ecommerce site, where I'm browsing to see what you've got to offer, and at what price, then you've just lost the chance of a sale by not supporting me on a mobile browser.
But if I click an email from your email http://you/richclient/whatever and get taken to http://m.you/ I will close the tab and never come back (and apparently Google will slap you around a bit)
After working for some time with iOS we recognized that an "app" suites our customers on mobile better than a "site". So we have a classic website for ecommerce, and a rich client application for mobile devices (HTML5, Angular). Both have very different domains and layouts, there is no 1:1 mapping possible except for the most basic features. The RIA page is optimized for gestures, orientation changes etc.
Contrary to mainstream opinion we believe mobile (for ecommerce, where people interact with a site, not newspaper sites etc.) is different from desktop (mouse, keyboard, large screen) and not just a "responsive" small version of your site (or desktop just a larger version of your mobile first site).