I'm sure it does exist in the form of a tiny chinese foam rtf that will not handle even the slightest breeze and will likely be destroyed on it's maiden flight due to the shoddy construction on the plane combined with a lack of pilot experience. Most planes cost more than what you're looking to spend, even for the really low end stuff. You might want to lighten up on the looks requirements and focus on the flying characteristics of the planes that you're looking at. You definitely get what you pay for in this industry.

As suggested earlier, a spad would fit your requirements if you're willing to build. They're not as pretty, but they're tough and dirt cheap to rebuild after a crash. For $100, anything that looks like a real plane is likely to contain very poor quality parts.