Well, "free" means there is no consideration on the part of the party receiving what would be deemed as a gift. Looking at ads and having your data sold is not free by any means.
If you want to repurpose the word to mean "free with no ads" you can do that, but you can't expect others to hold to that definition.
"Free" and "ad-supported" mean completely different things, and always have done.
"Free" in the context Amazon is using it (what Richard Stallman would refer to as Gratis) means that I do not have to pay money for something. That is a literal economic/dictionary definition.
Therefore, ad-supported in this context is a subset of "Free," as is any other form of non-monetary subsidization. So long as the end user is not paying, it is free.
The Free Software Foundation is free, but not ad-supported (though it strives to be free both in the sense "libre" (open/available) and "gratis" (not costing dollars).
If you show ads you're costing your users brain cycles and creating distraction and friction. The cost isn't monetary, but it's still a real indirect cost.
If it wasn't a real cost, ad-blockers would hardly be as popular as they are - and the ad industry wouldn't be quite so worried about them.
IMO the idea that anyone can believe the two models are identical from the user's point of view is not encouraging.
It's not free if I have to spend time servicing your revenue stream, unless you reimburse me at my market rate for my time that you spent/wasted.
To act like that is not a real cost is...baffling.
wut?
The way Amazon is using "free" the definition means that you don't pay money for it. Full stop.
There are other ways of calculating what your "costs" are, such as including opportunity cost (what you're referring to as "time wasted." If you use that definition of "free," literally nothing is ever free, as you're always forgoing something else.