No it's not. The H-1B program has no requirement for a labor market test (i.e. showing that there is no citizen that can do the job). The Immigration and Nationality Act, which is the source of the H-1B program, does not have such a requirement. The only big requirements are that the job require a degree (except for fashion models) and that it pays the prevailing wage.
I would have been more against it if I realized that.
But there's a logical fallacy in these discussions in which people criticize the current H-1B program for not being compliant with some made-up version of what the H-1B program is. If you don't like the current program, the solution is not "we need to do what the law says" because in fact the current program is 100% compliant with the law. The solution is to change the law.
(Not trying to be pedantic but US immigration law is full of random loopholes and people who qualify for them, or might be able to qualify with a bit of work, often aren't aware.)
I get that people like semantically and logically simple ideas, but the world doesn't reflect that.
Cost is an inherent part of the H1B program