Some of the user-unfriendliness is probably rooted in the perceived inconsistence of user experience. With conventional payment processors like Paypal you do everything in a single environment. Create account, deposit money, send payment, receive payment, everything is done using the same interface. To use a standalone Bitcoin client you not only need to install software and setup secure backups, you also have to choose a currency exchange service. So you end up using at least two seperate and different user interfaces.

OP asked how Bitcoin can improve the situation and in this regard the answer is it can't, because this is the very foundation of how Bitcoin works. Available standalone clients are already pretty straightforward to use, so there's little room for improvement.

However, most computer illiterate people may choose to not use a standalone client but rather the webwallet supplied by their currency exchange service. Though they surrender some advantages of Bitcoin, they can have a consistent and familiar user experience, which is highly important. An account-based webwallet is quite similar to a Paypal after all.