From ESTA Frequently Asked Questions:
What is the difference between an ESTA and a visa?
An approved travel authorization is not a visa. It does not meet the legal or regulatory requirements to serve in lieu of a United States visa when a visa is required under United States law.
So, wherever in US law it says things like "visa holder", this wording would not cause those laws to apply to ESTA holders also.
If somebody were to redesign the US visa scheme from scratch, they would probably find it simpler to have a way to apply for an "electronic visa" online, like many other countries do. But US law is very complicated and perhaps nobody has the energy or will to go through the entire legal system to fix things to make it simpler.
