All I can say about this is that plenty of people *plan* to do it, and almost no one actually does. Make of that what you will. My take is that after 8+ grueling years of training, most of us are pretty damn sick of living on a tight budget and a cushier lifestyle feels like a just reward for all those tough years of delayed gratification. Also, once you're through residency, most people are way past ready to get started on their adult lives: getting married, having a kid or two, buying a house, making up for lost retirement savings. What you're proposing is possible, sure, but it's much harder than it sounds, I think.
I'll use myself as an example, because I'm matching this year. I owe $50K, all in Perkins and subsidized Stafford loans. All throughout medical school, I planned to pay this off either before graduation or during my intern year. Now that I'm nearing graduation, that's looking less and less likely. For one thing, I have a child now. Daycare is unholy expensive. For another thing, real estate prices in the area where I'll probably match have taken a serious tumble, so now my husband and I are considering spending the cash we've saved to throw at my student loans on a down payment instead. The increased expense of a potential mortgage will make it much harder to pay down my student loans by thousands of dollars each month. Plus, I'm imaging my life as an exhausted resident and I'm realizing that I'd rather pay off those lonas a bit slower and spend some money on a housekeeper or a more generous food budget (more convenience food, more take-out). And while I'm being honest, I'll admit that I'd like to take my little family on a nice beach vacation (Hawaii or Mexico, maybe) duing my precious vacation time during intern year. Life happens, you know? It's very easy to imagine that you'll stay on a strict budget indefinitely, but it's hard to actually do it.
Also, don't forget about taxes. Once you're an attending, if you're single with no kids and presumably you're renting a place to live (since you're "living like a resident"), you're going to pay 35-40% of your income in taxes. So there goes, say, $75K of the $200K. Now you're down to $125K ... if you pay off $90K/year, that leaves $35K to live on, which is probably close to what you were making after-taxes as a resident (none of this "double" your residency salary business). So in your case it'll take two additional years or so of "living like a resident" to pay off the loans, assuming that your estimate of $180K is a good estimate of the capitalized amount when you finish residency. If you arrived at that figure by multiplying your MS1 borrowing by four years, it's way off. Even so, you could probably eliminate the debt in 2-3 years post residency if you were making $200K and literally didn't change your lifestyle at all.
Good luck. I'm sorry to be discouraging, and maybe you really are the person who can pull this off. But you're certainly not the first to consider it.