What I object to is mainly assimilating not paying money and being free : it's not free if there are ads, you're paying with time, mind share (because there would not be that much money in ads if it was not at least a little bit effective) and potentially security (as ads are a known malware vector)
That's why I insist that free as in no money is a very restricted definition of free, and should not be considered equal to simply free, because it then undermines products that actually are free
As things stand, they have ads, which require your attention not your frustration. That means time paying attention to the ads in addition to the time spent playing the actual game.
And you keep referring to the price tag, but as everyone in software knows there are different meanings of 'free'. Not all of them refer to money, but all of them are important to understand.
In this case the argument is clearly about things like child-appropriate content; at which point there is a clearly valid need to distinguish between ad-supported and non-ad-supported apps. You can argue about what to call them if you like, but 'free' and 'ad-funded' wouldn't seem far from the mark.
"Free" as in other-currency-than-money isn't free.