I don't even have a computer. I'm one of the people bitcoin is trying to win over to make it more mainstream. I'm not really tech savy. One thing holding bitcoin back is it seems you need to be somewhat tech savy to use them.
The same could be said about the internet in the 1980's. Bitcoin is still in its infancy as a technology and a protocol. Mainstream use will come later. There is a LOT of innovation that needs to come first. Of course those entrepreneurs that are able to provide that innovation will be the billionaire owners of the technology and finance companies of the future.
They recomend you don't keep your coins on a exchange due to hackers. Ok, so I send them to my phones wallet. Ok, now if I lose or break my phone my coins are gone. Not going to walk around with thousands of dollars in bitcoins in my pocket either. Ok, so now they say you need to back up your keys with a flashdrive or external hard drive, computer, or print out a paper wallet. WAAAYYY to many steps for your average user.
Not all of those things are necessary for everybody. It really depends on your personal needs.
Many people who have less than $100 worth of bitcoins that they won't be devastated over loosing are perfectly happy to store them with blockchain.info and access them through their phone.
If I have U.S. dollars, they reccommend that you dontt store them all in the stock market due to volatilitiy, Ok, so I put them in my back pocket. Now if I encounter a pick-pocket, they are gone. Not going to walk around with thousands of dollars in my pocket either. Ok, so now I need a safe in my house, or a security guard, or an alarm system. WAAAYYY to many steps for your average user. (And yet, many people seem to figure out how to use cash just fine?)
Until further innovation comes along, it really is a LOT easier to manage and secure your bitcoin finances if you have at least one computer. If you are trying to secure a large value of bitcoins, it's significantly better to have 2 computers (one that can be kept offline at all times).
It really needs a US based coin exchange thats regulated that people would feel safe keeping there coins in a online wallet then transfer small ammounts to there phone.
What you are describing is essentially a bitcoin "bank". Something regulated, insured, and audited. I'm sure it will come along eventually, but it will take a while. The financial world is slow to adopt new technology and paradigm changing concepts. We are probably many years away from something like that, but when it happens, it will be a MAJOR shift in the world of finance.