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).
Conversely, Android does allow 3rd party apps to swap out core parts of the experience and it has lead to some highly innovative products. Apps like Viber integrate VOIP into the standard dialler. There are countless SMS apps which add stuff like emoticons & IM functionality (even Google Hangouts is one). There are numerous desktop replacements, many which provide a modern launcher to older devices, or augment the experience in interesting ways.
Yes there is malware lurking around on the fringes, but that's the price of freedom. Google has a responsibility to squash it whenever it rears its ugly head in the store and I assume they're pretty good at it. Consumers have a responsibility to read the permissions and favour apps which have no earthly reason to be asking permission to do things which could be harmful.
I don't see they can do much for 3rd party stores. It's not Google's job to police Amazon's appstore, or Opera's, or the gazillion stores in China. That's their job. There is nothing to stop some Chinese entrepreneur launching a curated store with trusted apps from trusted sources. Maybe it already exists and some fools still choose to ignore it for another site where everything is free. More fool them.