Are there ways to reduce the size of the block chain? Or will we get to the point where only large service providers can hold the block chain? I ask because I was maintaining my own wallet for awhile but stopped because the block chain database was getting unwieldy - it would take up to a week to resync if I ever turned my wallet software off for a significant amount of time. You know though... I actually don't care.…
The basic idea is that bitcoins are actually units of money that are in your wallet. Rather bitcoin works by chaining transactions (put into blocks, hence the blockchain).
Thus if you give me $1, I don't have $1, I actually have a record that you gave me $1 so that must mean I have $1 to spend. That's the simplistic idea.
That is the reason why instead of storing account numbers with money numbers in them, bitcoin stores transactions.
By now it's probably obvious to you that the vast majority of those transactions don't need to be stored. If I give you $1 and you give it back, repeat 1 million times, we end up with exactly the same amount of money. And all but the last few transactions can be reasonable deleted. (pruning)
As for syncing, syncing up a wallet is much, much faster now that it's headers first. But most users never sync, they either use 3rd party wallets like Coinbase, or they use wallet software that plugs into various nodes and APIs, so that no blockchain has to be present on-disk. The blockchain is really stored mostly by nodes, dedicated servers, businesses, a few enthusiasts.
That doesn't mean someone else manages the wallet by the way, like you mentioned for 'consumer devices', it just means that someone else manages the node. But the node doesn't control your money, your private keys do, and those are just a few bytes of storage. And as there are thousands of nodes and many APIs, trust of nodes isn't any different as when running your own node (which gets and sends data to other nodes, requiring the exact same amount of trust which is zero when it comes to controlling your money).
As for transaction fees being expensive, they're extremely cheap? Pennies to send thousands or millions, and as it's an open protocol anyone can build free centralized payment networks on top of it, like Changetip. Conversion with other currencies is also cheaper than most fiat conversions (e.g. dollar to euro), and in fact some companies already offer it for free (e.g. bitcoin/usd is completely free and pretty much instant with Circle, founded by Jeremy Allaire who founded Coldfusion).
The 15minute thing might be a deal-breaker for some. There are lots of solutions though that can remove that timer, built on top of bitcoin. Sidechains, treechains, payment channels etc. Anyway time will tell if these things work well but there don't seem to be any dealbreakers yet on the horizon.