It probably doesnt hurt sales a little bit.
But I remember someone once saying Amazon was only ~5% of the games market in the USA.
And like you said, people that cant find it on amazon, most will probably just go look elsewhere.

There's definitely an issue between them and it's more than likely Amazon refusing to stock. 

Amazon would not want to restrict 3rd party sellers from selling the PS4, just because they can, either. They would receive a huge backlash that would do more damage than good. 

It would hurt PS4 sales a little but Amazon will definitely come off worse. The question is why are they prepared to lose hundreds of thousands?

If there is a bigger end game in sight. It s not something they would undertake for petty reasons though.

Personally I am not sure about the Amazon/Sony speculation, the PS4 supply has been anaemic in Japan before now, its very concievable the issue goes beyond a squabble with Amazon.

The Japan situation was because of short supply in Japan. In the US there isn't any supply issues. Also, it's not just the console that's just had stock issues on Amazon, it's also exclusive games and digital codes. 

There was an article on it.

http://www.pushsquare.com/news/2018/04/playstations_relationship_with_amazon_worsens_as_psn_codes_are_dropped

Yeah, forgot about the PSN codes thing, that seemed to be resolved quite quickly though.

I still see no reason why Amazon would deliberately miss out on PS4 sales though, makes little sense really as the damn things are obviously still selling gangbusters.

Depends.

If Sony for instance would have cut down a more or less large chunk of the retailer margin, shops like Gamestop are in no position to argue as it still represents the largest part of their income by extension (selling hardware means selling the same customers the games also most of the time - and it's the games which normally have the better margins for retailers) but Amazon or Walmart who sell lots of different things have stable income from other stuff they sell and thus can fight back like not stocking Sony articles anymore.

I did not expect that! SNES games still selling, lol

That's a good point. 

PS4 games "stock issue" are always resolved the day of, or after release date. Detroit got stocked exactly on release date. Ironically pass the pre order 20% off deal.