It might be for fairness between free and paid apps. If it were so much easier to install a free app, everyone would do free apps with ads and IAPs. Apple likely prefers having apps show their price up front, for good store UX.
I assume it's due to the free apps ability to make in-app purchases and if you have a child using your phone they could rack up lots of charges without ever identifying if there was no password to download the app. If the password was when making in-app charges it would be more of an annoyance than entering once up front.
In app purchases require a password anyway. I really dont see the need for passwords for free actions. Android hasn't needed a password in those cases.
It's unfair to paid apps. I think during iOS 6 beta they tried no-password-asking-for-free-apps policy, paid app developers didn't enjoy.
I suspect it ensures you authorized the app to be on your phone should any liability, or other legal issues arrise. Buddy downloads OKCupid onto your phone, Wife sees OKCupid and files for divorce and takes everything thanks to pre-nup. Man sues Apple for allowing app to be added to device without his consent.
Buddy could add a shortcut to http://OKCupid.com to friend's iphone home screen and accomplish the same thing, without password.
The password isn't just about accessing your account information (making a purchase), it's about authorization to use your hardware.
OSX does the same thing: want to install something? Enter a password.
I agree that there should be a better form of authorization than password, though.