Are most websites run by businesses which employ 15 or more full-time employees?
To be illegal the website must be run by a business which employs 15 or more full-time employees. Or the business is some form of public accommodation like a hotel. From what I have read.
Of course it would be better to make sure the website is accessible, but I'm mostly commenting on the statement that it is illegal.
In the US, it is if you're an incorporated business serving as a "public accommodation" as defined in the Americans with Disabilities Act, which includes hotels, restaurants, theaters, storefronts. If it is just your personal blog, it doesn't apply. It is the same law that requires storefronts to have wheelchair ramps, but not homes. See Gil v. Winn-Dixie: https://scholar.google.com/scholar_case?case=674450226911160...
More than that; as someone else linked [1], if you're in a business employing at least 15 people (more than half the year), you are also required to have your site be accessible. You don't have to be serving as a public accommodation, for that.
[1] https://github.com/markets/invisible_captcha/issues/52