Sounds a lot simpler than it actually is.
Amazon has a Most Favored Nation policy which means sellers can't sell for cheaper elsewhere than they can on Amazon. This includes most coupons/discounts.
A good example would be Anker. You can Buy this power bank for $180 on Amazon, or $230 on their website, but with a discount code that only goes down to the exact same $180 price on Amazon, and is just there to make you hopefully choose to buy from their site in the future thinking you're getting a better deal. You will not find a discount on their site that goes lower than the Amazon price for that same item and colorway.


If brands add coupons that drop prices lower than they sell for on Amazon, Amazon will delist them from Amazon entirely and they'll lose most of their customers.
Now, consider that most people will either already have Prime, or will probably get at least the same minimum order value for free shipping on Amazon, but will be able to add items from ANY brand to get to that minimum, compared to other seller sites that obviously only sell their own products, and most people will end up paying more for shipping too.
It's reasonable to do if you're willing to spend a few extra bucks in order to give a company a substantially larger share of your money because you want to support them and not Amazon, but it's just not tenable for most people when they have to pay an additional $6 per brand they buy from with every order for shipping, not to mention that a lot of brands just don't even bother to price-match Amazon discounts on their own sites, meaning they can sometimes be more pricey than just buying from Amazon.
If I'd purchased everything I bought on Amazon in the past year from other brands, I'd have paid over two to three hundred dollars in shipping alone given the variety of brands that I get things from that I would not be meeting the order minimums for, not to mention the prices often not being as low as Amazon's since they don't bother updating their site as much. I wish I didn't have to buy from Amazon, but I also can't afford spending hundreds of dollars in exchange for nothing every single year to do so.