@mckenzie,
mckenzie-
Thank you. I believe your reply is the most helpful.
Of the four persons to reply, only you are a court reporter.
You state that the fee is payable directly to that attending court reporter. Your statement contradicts the other answerers. As a court reporter you would know.
Perhaps the correct answer varies with the particular municipality, county, state, or federal government.
You are silent on who sets the price of the transcript. The government entity? The particular court reporter? Does the court reporter get a salary and benefits also? The general rule of law is that if an employer pays an employee than the fruit of the labor belongs to the employer.