It's not, but I don't want to work for someone that demands to know what medical procedures I've decided to take or have done.

Sure, but I assume if they are asking they want to see some kind of proof. That could be nearly impossible to fake depending on how they do it in your area.

recruiters pays the double of money

A lot of companies only go through recruiters these days.

I personally feel this is one of the reasons (albeit a minor one) that companies can't find qualified employees.

Recruiters often have no idea what they're recruiting for and continually bombard candidates with positions that don't match skillsets - and then ghost candidates if they do call back and aren't 128% perfect. Even worse is that a lot of recruiters are thinly veiled offshore companies. They have an office in Houston or New Jersey and do all their business out of India - these people are useless, and they don't even understand the words. They're just parroting keywords and things they've been told which becomes evident when you get an email with all of the "your eyes only" information left intact.

Even traditional onshore agencies like Half, Manpower, etc. are going the Indian route. I will say this makes them very easy to weed out and discard, the minute you see something like "Kindly respond" or "Hope this finds you well" you can discard it with absolutely nothing of value lost.