Most of these answers are pure opinion, based on American cultural perceptions.
First, I am married to a wonderful Ukrainian woman, and we do some translation, scam investigations, and interpreting work in this area.
A great majority of Russian and Ukrainian women do not have access to the internet, and have no idea such sites exist. Most of my wife's friends usually say they can not believe a man 10,000 miles away would want to meet a Russian/Ukrainian woman in real life.
Just like we have the false stories of "Russian Brides seeking green cards", they have the stories of "American men seeking Russian women for prostitution". Although this happened a lot in the past, it does not happen much anymore (at least with the US and Britain) due to the visa requirements.
The women do not view it as "degrading", they view it with disbelief. The Russian/Ukrainian men, on the other hand, view such sites as pure "prostitution". They also dislike "their women" being with Western men.
Most (if not all) of these "free dating" sites have nothing but scammers (and they are usually men, pretending to be women). However, there are many reputable sites. You will also find the newspapers there filled with advertisements from Western men looking for women. Again, the women do not believe that a man would really travel around the world to meet a woman.
As to the post that says "men going there must have problems meeting women in their own country", that is certainly a biased opinion. Most American women can not understand why men are drawn to Eastern European women, and most would call me sexist.
Believe me, no man would go through what it takes to bring a woman to the United States or Britain unless he was very serious with that woman. And quite honestly, it is difficult to find an American woman with the moral values that an Eastern European woman has.
If I was looking for a slave housewife, I certainly picked the wrong woman. I will say that under her guidance of our family, we have a healthy bank account, our bills are paid, our family is healthy, and we are both very comfortable with our lives. In actuality, we live in Ukraine as a choice rather than the US.