Bypassing the recruiter is a simple and obvious strategy that many companies would do if they could. Either by hiring directly, or by the sort of cheat you suggest.
At least in Australia many (most?) recruiters require the company to pay a commission for anyone they refer who is hired by the company, regardless of whether you approach the company independently. That's specifically to get around the approach you suggest. If you look through this search for "two recruiters want to send me to the same company" you'll see that that issue raises similar problems. In that case your idea just will not work.
From the company side, by doing this you're showing that you encourage cheating, and that may not be a characteristic they look for in employees.
You can always ask for a cut of the commission. I suspect you're not likely to get it, especially if you phrase it as you have done.
If you're contracting through a recruiting company it's often unclear as to how much of what you get is coming out of the recruiter's commission. From the employer's point of view, they're paying a set amount negotiated with the recruiter and how much of that you get isn't their concern. If you negotiate well you may end up with a bigger slice than some of your peers. I've done that in the past.
For a permanent position it's a little different, as they're getting a fee from the employer and you're getting paid separately. So you're very much asking the recruiter to give you some of their payment, and it's obvious to everyone who sees it what is happening. Unless you're a unicorn I can't see that happening, and you'd have to be a pretty special unicorn for the money not to come from the employer directly. Ask for a signing bonus, that's more likely to work.
The other approach would be to put it as a request for reimbursement of your expenses. Ask the recruiter to pay for your transport or taking the interviewer out for lunch or something. IMO that's less unlikely to work.
The ethics of those approaches are, as others have said, at best questionable. Cheating the recruiter out of their commission is somewhere between illegal and wrong. Asking for a cut of that commission is more on the unwise spectrum but it's ethically dubious in that it says you don't think the recruiter is entitled to be paid for their work.
That seems to be the thrust of your question. My answer to you is: if you don't think their work is worth paying for, don't use them. Don't apply for jobs through recruiters, and stop dealing with anyone offering work as soon as they make it clear they're a recruiter. It's that easy.