Amazon cares substantially about stopping these things.
As is the case when you are fighting against other humans, who are crafty, financially-motivated, and are willing to break the law, and may be operating from different jurisdictions where attempting to get the DA to prosecute them or filing a lawsuit against them is ineffective, it's a very difficult battle to fight.
As an example I'd be surprised if Amazon could get China to prosecute a business operating from their country that's selling counterfeits on Amazon. Additionally, it's hard for Amazon to know if a product sold in its marketplace is counterfeit: there's no global API or method to look up if a product is authentic. The best you can do is rely on the trust of the seller. If you want to mitigate your risk, buy products that are only sold by Amazon itself, or name-brand 3rd party sellers who have high reputation (like Belkin for electronics; Apple even lists Belkin products that integrate with theirs on Apple's online store: https://www.apple.com/shop/accessories/all/power-cables?fh=4... ).
People occasionally experience counterfeits, but once reported the seller is typically caught and banned. (But if they're a corporation in another country, and willing to break the law and ToS, they'll reincorporate under another name and try to do it again. Stopping this is difficult.)
Reviews are also a difficult problem to tackle. Amazon decided long ago to allow people to leave reviews without purchases, though reviews from people who purchased the item get an extra "verified purchase" badge. But that doesn't stop the abusers: they "buy" the item under various accounts they've created themselves, give the product a good review, and then return it to their own inventory. Small sellers might get a bunch of friends & family to do this, which would be hard to detect as ToS-violating conspiracy; larger sellers will use sophisticated schemes to create many accounts and identities to do the same thing (or simply pay a network of actual people to do it, such as by asking on Craigslist and similar places), to boost reviews of their own products, or if they're willing to burn cash, buy and negatively-review products of competitors. When done from many names/addresses/credit cards/IP addresses, it requires sophisticated intelligence analysis to detect and stop.
Please consider the attackers that Amazon is actually up against when trying to stop these abusive behaviors before concluding that they don't care. They have multiple hundreds of people working on the problems. They are simply hard problems to solve, because Amazon is fighting against other smart, sophisticated humans who gain financially from their abuse.
Amazon could shut down its marketplace, which accounts for 50% or more of all sales on the store, and only sell products it acquires directly from manufacturers, but that would destroy many businesses who have built themselves up using Amazon as a primary venue to sell their product. Furthermore, it would disallow people who have legitimately acquired the product another way from reselling it--for example, say I buy a pallet of some authentic product from a retail store that's going out of business; shouldn't I be able to resell those products? The law says that I can. If Amazon has a marketplace, shouldn't I be able to resell there? These could be Nike shoes or any name-brand products.
(Sophisticated manufacturers who want to protect their supply chains from 3P reselling will repurchase inventory from retailers who are going out of business; or alternatively provide it to retailers on consignment --meaning Nike owns all the shoes being sold in a retailer's store up until the point where they're sold to a consumer; so upon going out of business the retailer is expected to return the inventory.)
Now you run into tricky situations. I buy a pair of Nike shoes brand new from a retail store and never use them. I decide I don't like their look after all. Should I be able to sell my shoes on Amazon as new at a lower price than Nike does? Yes, you should and you can (though you're unlikely to be selected as the default offer as a new untrusted seller with a single product; unless Nike is one of the companies with brand protection for what may be offered as "new"; though I believe you could still sell as "like new"--I am not an expert on this space).
Some brands were counterfeited so frequently that Amazon has started to offer the ability to limit who can sell trademark-protected items that are only sold by their manufacturers with its Brand Registry: https://brandservices.amazon.com/
I believe the sellers who are accused of fraud or counterfeiting will be asked by Amazon to provide proof of authenticity, such as purchase orders from the manufacturer or other proof of authentic origin, but allowing people to open accounts and sell means they start with a presumption of trust -- creating the possibility that some people will have bad experiences with counterfeiters until they're caught and shut down.
Imagine you're the Amazon engineer responsible for figuring out how to stop people willing to break the law and all of your policies to make profit; then put yourself in an attacker's shoes and imagine all the things you could do to circumvent the best ideas you can come up with for stopping fraudulent reviews and counterfeits. (Assume for the sake of argument that your company is committed to allowing third-parties to sell on the store.)