They do exist. I have been in some in London, Paris, Frankfurt, the best in Geneva and Zürich. I am a lover of Chinese food.

The biggest problem is more of a cultural clash. I do not want to discriminate or offend anybody, but along my travels I have noticed that hygiene and cleanliness in kitchen are not a primary concern for Chinese, the world over.
There are countries however, where the health department is much harsher than elsewhere (Switzerland, for example) and this is one of the countries where I can almost vouch that ALL chinese restaurants are spotless. From the cheapest to the most expensive.

As far as the food is concerned, economics is the main judge who'll decide what is on the menu. There are many countries where chinese food is well loved, but in a mild form of exotism. Certain dishes could never be sold in say Germany or Switzerland.

I just came back from a trip to Japan and was confronted with beans that are a delicacy over there but just triggered a violent reproval from my stomach as soon as seen....

If you order in advance, I am sure you would have the possibility of getting anything you wish, but don't expect to find everything chinese in a "European" chinese restaurant...