Because the people who download dodgy apps and sideload them, then click past the permissions list without even looking at it would selectively disable the permissions they didn't really want to grant?
The permissions problem you refer to is a really difficult one to solve. Oh, it could be solved for you, by giving you the ability to selectively disable permissions (which, BTW, you can actually do with a small amount of one-time effort), but face it, less than 1% of Android users would carefully vet and individually select the permissions. Probably much less than 1%.
The problem is in China, Google is not allowed, so Android phones do NOT ship with Google Play. Instead they ship with one or dozens of official Chinese Android app stores, which have poor quality control, often contain pirated apps (submitted by other people), and yes, tons of malware. (It's also a failure of competition as each store competes for business, so they end up wanting people to post as many apps as possible so they get used the most).
Asking the user about security is a big no-no these days, because the user will pick the option that gets them to their goal to the quickest. Or, put another way, users will pick dancing pigs over security any day. It's a failure of security policy to not recognize this (think about all the times people workaround IT security restrictions just to get their job done).
The Android permission system is basically that policy - pop up that huge list of permissions, the user's eyes glaze over and they want to pick the option that gets them "Candy Crush With Everything For Free" the quickest. Well geez, what are they going to do?
Same goes for any popular app - recommend them a cool app and they probably won't look at the permission list at all.
With this in mind, on iOS, there's no API to get at the SMS directly - you need to rely on OS flaws to do it. Even sending an SMS requires switching to the iMessages app - no app can send an SMS directly unless they implement SMS functionality within themselves (which means they can't use the cell network SMS facilities).
In that case, Apple simply makes it impossible for the user to "do the wrong thing" under the assumption that 99% of the time, any app wanting to do this will use it for evil. Sure it keeps innovative SMS apps off the App Store, but developers it turns out that for every innovative SMS app, there will be hundreds, if not thousands of other developers who would abuse the privilege. (Especially for say, advertising).