While you will find all kinds of consumers, those who will stick to 100 year old brands and also those who will go for 1 year old private labels, what any platform like amazon cannot afford to do, at least for now, is that do not support sales of good brands. If they do that in any means, that will be an opportunity for the competitor platform to get the other set of consumers who are brand specific. This will result in Amazon loosing on their private labels random purchases…I can write a long essay on this but to be short and precise…this is a coexistence world and none can survive without the other, market is huge, runway is huge and any brand which constantly innovates, provides consistent and relevant value and makes sure it is available when needed will continue to remain core to the consumers as well as to the eCommerce platforms.
Small example, in current crisis situation why is Amazon still selling Safolla, Parachute, Harpic, Dettol etc. when they can make the most of it. The core strength and value proposition of Amazon is to provide platform and technology. If they focus more and more on manufacturing, private labels etc. then in next few years it will give rise to some other Amazon who will be selling other popular brands. They would never want to lose their core competency to someone else for the greed of Private labels.
Having said that, there would be some categories which will be dominated by private labels in Amazon, Walmart, Dmart, Star etc. and agilent FMCG firms will slowly reduce incremental investments in these categories and focus more on those where a retailer does not have the core competency to provide better value to consumer.
With time, none can survive without other and none can kill the other. What they can very well do is kill themselves by overdoing something which was not supposed to be done.