You have been given some misinformation. First, close bird relatives mating is not the same as mating defects or abnormalities which usually can occur in mammals. We have seen siblings mate and produce for years with no genetic defects. So, to allow her to produce eggs is not a concern.

The major concern is you are taking the eggs. A female bird is programmed to lay a certain number of eggs each year, culminating in the total amount she is programmed to produce in a lifetime. Therefore, each time you remove the eggs, she will produce an egg to replace the one you keep taking. The problem with this scenario is that a female swan loses approximately 30% of her energy levels during the nesting period. So, your swan is losing a lot of energy to replace the eggs and can get a stress related illness or other health related issues which could lead to serious complications such as egg impaction. The bottom line is to let nature take its course and do not intervene. The Regal Swan