Examples:
-esp8266
-RTL8710
-Atheros AR9331
-Any Allwinner SOC

The completely obvious ones are Ebay, Aliexpress, etc...

I'm not actually asking where to buy them, I'm asking about a legitimate place to buy them. There's no disputing that buying parts from vendors such as Digikey, Arrow, Mouser gives a certain level of confidence that you will have a stable supply in the future - this is in contrast to some shady ebay individual that may or may not be around tomorrow.

Are there certain quality control issues with the manufactures that don't jive with the vendors? Or do the manufactures only sell in massively high volumes? (that eventually trickle down to small vendors) - I thought Allwinner's SOCs were built into most Android tablets??

My question / point of conversation is: If I was a company designing a tablet, where would I start if I wanted to design around some of this silicon? Contact the companies? Just buy from shady vendors?

Is there a centralized location where I can browse all this ridiculously cheap stuff? With a price tag on different quantities etc?

 

There is no good answer to your question. A small company cannot afford to waste time screwing around looking for and qualifying low cost vendors. For 100 pieces a year you buy from an established distributor, you pay their price, and your customers pay your price. For 100,000 pieces a year now you can afford to shop around. What you do in between varies a great deal. We never made it to 100,000 pieces a year; 1,000 was about are maximum. When the vendor refused to deliver after a 26 week lead time had expired we ditched them, redesigned the product, and never looked back.