I have to step in on that one myself. The answer is the very reasons we all do conversion engines. One is cost. A conversion engine, even if it needs rebuilt, will cost a small fraction of the cost of even a Chinese purpose built engine. (Many people get the engines themselves either for free or a token fee. So the only cost is the conversion or rebuild parts.) I myself often sell complete, ready to fly converted engines for around a hundred bucks or so. You won't find a purpose built engine for that price.
Another is "just for the fun of it". It is very rewarding to take an engine and re-purpose it for your airplane. Then there is also the "wow" factor when you tell people that the engine on the airplane they just saw fly, came off of a (weedeater, leaf blower, chainsaw, etc.). This is quite fun and rewarding as well.
Lastly, is quality. The Stihl, Echo, Homelite, etc. engines we all tend to use are of considerably higher quality than any of the Chinese engines, and will be more durable, especially at high rpms. I should add that a properly hopped up conversion engine will also be more powerful than the Chinese engines, as evidenced by the performance of the engine I posted about above.
AV8TOR