Even for those of us who are computer savvy, the lengths you have to go to in order to make sure that your wallet is completely secure and redundant isn't easy. I feel a lot more secure with the bank holding my money.
This is why the whole notion of Bitcoin's success is paradoxical. To really succeed it probably has to be pushed by these third-parties, which is an advantage over our current banking system because the core protocol will still be neutral, but only to an extent: third parties will almost certainly build features that lock people in on top of it. This is a far cry from the vision some proponents have of a completely decentralized system.
This level of user verification, necessitated by KYC, AML policies and so on, is extremely burdensome for end users.
In fact, I've heard Coinbase is now requiring their users to declare exactly _where_ bitcoins are to be sent when a withdrawal request is made. Furthermore, Coinbase is having to shut down customer accounts that are known to be associated with online gambling.
Native wallets don't come with these "features". That's the benefit of being in control of your own money.
If Bitcoin ends up relegated to native wallets it probably will look like TOR - something that tech savvy people can use for certain activities, but not something that really caught on in widespread use.
Being able to be in control of your own money is great, if you can do it, but I tend to think most people don't want or can't handle that level of responsibility. Kind of at the heart of Bitcoin is a very libertarian philosophy on life and government. Our political system shows us that the vast majority of people aren't looking for that, and by extension, it probably applies to financial matters as well.
Why?
Using bitcoin for currency as a whole (IMO) is almost like a misguided application rewrite -- sure, at the beginning it has all these advantages of being light and nimble and having limitless possibility, but by the time you add all the stuff users actually want/need back into the system you wind up pretty much right back where you started with the old heavy app, perhaps with a shift of power behind the scenes (from the old architect to the new architect, if those are different parties), but nebulous real advantages for end users at the end with a lot of transitional pain in between.
3rd party wallets do not provide security via black magic. They use tools like passwords, 2FA, and email addresses, all of which could be compromised on a user's computer. Think key loggers, viruses, social engineering, people leaving their computers unattended with the wallet open.
There is no technical reason why the security measures that Coinbase implements cannot be done using a personal wallet. Moreover, when storing coins on Coinbaes, you are additionally subject to counter party risk (Coinbase goes under, loses their coins) as well as regulatory risk (Coinbase shuts down withdrawals due to regulations).
Yes, they use passwords, 2FA, and email addresses, but those are all things mainstream users are familiar with and have to use for any other major service. They are not familiar with the concept of encrypting a wallet or the fact that deleting a wallet can lose you money.
Of course you are at risk of something bad happening to Coinbase, but steps like getting insurance are hedges against that. I should point out that when I talk about mainstream users, I'm not so much talking about right now, but in potentially a few years when Coinbase is more of a known institution or existing banks or other parties have jumped into the game. At that point a wallet hosted by Google or something will be a much better bet for most consumers.
Yes, and they can do that without handing over their private keys (see blockchain.info, etc.)
The problem is that Coinbase only insured themselves against damage from coins-in-transition being accidentally lost or being stolen. That doesn't actually cover most of the cases that I'm worried about, because while a 3% loss would be annoying, it's nothing compared to the other failure modes and should be a loss that's sustainable by Coinbase independent of this insurance policy.
The problem isn't fundamentally exchanges holding the coins, but rather, exchanges holding coins so irresponsibly currently.
The fact is that web wallets are available that are just as user friendly as coinbase that don't require you to do this. (trust a third party and/or stab yourself in the eye)
Of course, bitcoin startups really want to use the second model, where THEY control the money, which gives them many more avenues for profit: As any salesman knows, the closer you are to the money in a business, the more money you're likely to make yourself.
This means bitcoin companies are bending over backwards to say "look how safe your money is!" However, be aware if you ever buy bitcoins, it is much better to store your own bitcoins or use a wallet that allows you to manage your own private keys, or use a (now trendy) multisig wallet where the wallet company can't move money without your permission.
If a bitcoin bank says "We insure our bitcoins" your best response is "No thanks, I'd rather not have to trust you with my money in the first place." The whole raison d'être of bitcoin is that such trust isn't necessary.