Linux survived these attacks. Debian survived them. Ubuntu did. More or less all Linux distributions have been attacked but survived, many of them thrive.
Yes, this is free software. Being less susceptible to these problems has been one of the stated advantages of using such for a long time. Alternative 'stores' carrying 'pirated' non-free software do not have this advantage and can easily turn into dark places so the solution does not lie there.
Will people choose a 'boring' free software 'store' over a 'cool pirate store' (Arrrrr!)? Some will, some won't. Those who will will end up being mostly silent as the thing just works. Those who won't will be susceptible to the whims of those who put up those 'stores' and are likely to come home with a bit more than they asked for.
Some 'stores' will get a good reputation along the lines of that of F-Droid, some will get the reputation of being the place to go to get the latest craze but also the latest infection. Users will start making conscious decisions based on those reputations, just like they already do elsewhere.
Will opening up closed platforms like iOS for third-party software repositories get rid of these problems? No, it won't, it will even raise the average level of problematic software on that platform. The difference between closed systems and more open ones is not that the closed ones are inferior, it is that they limit the user's choice to get something which is better as well as worse than what the walled garden offers. In this context better can mean software which does not come with tracking, analytics, profiling and other such privacy-invading nonsense. I can get the source code and build it myself, I can host my own repository, only time limits where I can go. This is not true for the Google Play Store or the Apple Appstore, nor is it true for the Amazon equivalent or any of those Chinese alternatives. That is why I chose to use something like F-Droid.
By the way, there is nothing keeping e.g. Facebook or Twitter from releasing a free software version of their apps. Their value - and most of their profiling proficiency - lies in their platforms, not in the apps used to access them. They might lose any additional venues for leaching the user of data but they would gain some believability when they state that they're not up to no good. Of course there are plenty of alternative apps for these services so they don't really need to but they could if they wanted to.