Amazon is my default place to buy just about everything. I'm a big fan of Harry's for all of my shaving products, though. The products are great quality at fair prices. They are not sold at Amazon. Brands like Harry's are, in my opinion, a big threat to Amazon long term.
Does Amazon sell shaving products? Absolutely. Do they sell Harry's? No, they do not. It doesn't matter what prices that Amazon can sell razors for because they don't carry the brand that I want. In talking with my wife, she said there are a number of makeup brands that she prefers that aren't on Amazon (unless it's a third party seller, and they are usually knock-offs). They only are sold through makeup specific retailers.
Amazon, in some ways, relies on brands not mattering to the customer. What they rely on is you trusting the Amazon brand and the Amazon shopping experience. Amazon's biggest threat isn't Apple or Google, it's everyone else. As Amazon continues to grow as a store, they are open to smaller brands chipping away at their retail dominance.