All the web has to do is figure out why people will spend $1 at a vending machine for tiny terrible snack that is completely unsatisfying but won't spend $1 on a mobile app that they would use every day.
1. Snack food is very highly consistent. As with other mass-market goods, it's entirely homogeneous. You know precisely what you're getting. Information goods are virtually by definition not homogeneous. Virtually all successful sales models for information goods are based on some level of subscription or branding (frequently by author, venue, or publisher/publication, particularly periodicals).
2. The typical vending-maching payment mechanism has no extended-tail risk. Deposit a few coins or bills, receive your product (yes, I suppose there are debit/credit based vending systems). Every time I make a debit or credit card payment, particularly online, I'm creating a risk of future account fraud. That's something I weigh heavily, have experienced in the past, and quite simply do not consider worth any putative convenience benefit. Paying cash is a very reliable stop-loss risk mitigation strategy.
3. Privacy. Particularly for information goods, leaving a perpetual trail that I specifically paid for specific items of content is ... highly unappealing. I don't pay for my physical books with credit (or use "loyalty", a/k/a Snoop Card programs). It's why I don't and won't use Kindle or similar apps (I do read eBooks, but open, untracked formats, on other devices).
Oh, and I really don't buy much from vending machines. Prefer fresh foods or a good street vendor if I can find one.
If only apps were that way. "I feel a visceral need for a new app, and if I don't get it somebody is going to get hurt!"
I would pay .02$ for displaying a news page (it's is still 4 times more than what advertisers give to publishers) and probably everyone would - but disrupting trillion ad business is not that easy.