It is security - they don't want the ability for downloads to come from anywhere but iTunes or directly on the device. How else do they make sure it is legit software and not someone spoofing a legit store
You're not thinking 3Dimensionally.
When you sit at your iPad, open the app store on it and select an app to install it's all wireless nowadays over your wifi. They know it's you because you logged in to your iPad.
Now, Apple allow you to authenticate on the web to do things such as
Update credit card information
Change passwords
Wipe entire devices
Delete your ENTIRE Apple account.
Therefore, Apple are comfortable trusting you are who you say you are over a https site.
Why can't there be a login to store link for each application page?
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OP is saying it's 2016, why can't he do it the way he described, which is something various other platforms support, but not iOS.
There's always one, in the old days, a lot more. Im glad to see that for the most part it's just people having a discussion.