These aren't contractors like Uber drivers. They are corporations that are contractors of Amazon, and the drivers are employees of those companies. How would this possibly be a legal issue?
But the government doesn't tell those companies "you cannot work for anyone but us." The government doesn't tell those companies "your employees must work these hours" (it may say "we require coverage for X period of time").
And so on.
This is the same situation when independent contractors have only one client.
When companies like Amazon buy other companies and vertically integrate, people complain. When Amazon contracts with vendors instead, people complain too. I don't think there is any legitimate point to this and it's just "I hate Amazon."
They're setting up these companies as part of their DSP program to limit their liability. They're following the chicken industries playbook(which shouldn't be legal either) by requiring the DSP use Amazon equipment, with a loan from Amazon, pay back by revenue from Amazon.
They're also using this as part of an anti-unionization strategy. One of their DSPs recently unionized and Amazon just cancelled their contract.
https://www.theguardian.com/us-news/2023/jun/24/amazon-deliv...
These employees are Amazon employees in all but name.