The rich may leech off the system, but so do the poor. I see examples of it nearly every day. Which is why there shouldn't be any system to leech off of. Not abolishment of government completely, but certainly downsizing it from the ridiculous bloat it has become. No welfare or loopholes for anyone, rich or poor, to use.
The poor don't ask for Trillions They Already Have, however.
Also, here's a cool chart from Moody's, showing the estimated return rates on investment in social programs; many of those you lash out against have POSITIVE returns (if you're wondering how, it's mostly to do with enabling workers and businesses to continue working or have infrastructure):

I am fine with my return off of labor. I wouldn't mind more money, but who would? I got myself a degree, I work hard, and I take home a decent paycheck. I put some into a retirement fund, and at some point when I have more of my debt paid off, will start putting more into more savings accounts. If I get cancer and none of my family can afford to pay for it (or wants to pay for it), then I die. My wife would have life insurance payments to help take care of the children and pay off the mortgage, because I was smart enough to pay for some, and life moves on. If a person puts their family's financial state into danger because he didn't pay for life insurance, or assure them other means for survival should he pass, then that is his fault.
If you "didn't want to pay for cancer", there's a good chance your life insurance has a clause that would let them rule that suicide or something, I'd check that. (Suicide means they don't have to pay out)
Also, one of the big reasons why a cancer care bill might run into the hundreds of thousands is because many people never pay their hospital bills. Remove that leech of the system, and you'd have much smaller and more manageable bills for the people who actually do pay them.
Single payer effectively fixes this, as the hospital gets payed regardless of the customer.