The lack of wallets for iPhone and iPad may be one of Bitcoin's biggest hurdles to mass adoption. Many early adopters use Apple products, but much of Bitcoin's appeal is lost if you can't carry it in your pocket. It's part of what makes Bitcoin cash-like.
Coinbase is already unsatisfying, as far as software wallets go, because you have to register with an email address. Your coins are held in a shared wallet, not on the device. But at least you get the idea of how Bitcoin works on a phone.
On the other hand, Apple didn't explicitly design iOS to be a highly secure environment suitable to store digital money on. A couple months ago, a bug in Android's random number generator was discovered that compromised all key pairs which used it. Android wallets had to issue an update which moved all the bitcoin in each wallet to a new address, generated with the patched RNG. But for a day or two, most Android wallets were vulnerable.
You need a wallet to make purchases using your phone (i.e. a wallet with its own address to transfer from or to). It's just like carrying cash. I can't transfer cash from home once I'm at the store, I need it right there. So what I do is usually transfer some bitcoin from my "main wallet" to my "phone wallet" when I think I might need it. If there are no wallet's for the iPhone, however (I use Android so I have no idea if this is actually true), then bitcoin on the go is useless to me.
Bitcoin is now > $400, it's well past early adoption stage. That was back in mid-2011.
( As an example, I did a technical presentation about Bitcoin to ${WORK}, a very traditional financial services company, in July 2011. Even then and in that context it wasn't a startling new concept. )
What's occurring now is the 'gold rush' stage, in which mid-curve-technology-awareness people are willing to use whatever technology is necessary to secure some Bitcoinage. I don't think the lack of iOS wallets is hindering that.
For storing $40 or so (like cash in a wallet) iOS's keychain should be plenty secure. For larger amounts the Coinbase method seems pretty good. They don't have to trust the device.
There are two wallets available in the app store. Blockchain and Coinjar. I can attest to the security and great UI of Blockchain. I don't know anything about coinjar.
Is there anything a native Bitcoin app could do that a web app couldn't do without a proxy to the Bitcoin network? (Which is what I believe Coinbase does anyway)
Coinbase is already unsatisfying, as far as software wallets go, because you have to register with an email address. Your coins are held in a shared wallet, not on the device. But at least you get the idea of how Bitcoin works on a phone.
On the other hand, Apple didn't explicitly design iOS to be a highly secure environment suitable to store digital money on. A couple months ago, a bug in Android's random number generator was discovered that compromised all key pairs which used it. Android wallets had to issue an update which moved all the bitcoin in each wallet to a new address, generated with the patched RNG. But for a day or two, most Android wallets were vulnerable.