I would say that it does seem that we agree on the basics, but not on the details. And your point about each person making their own choices is of course quite valid. We each have our own ideas of how to make this multi-cultural, multi-national relationship work. Personally, I do not consider men and women equal in the sense that they are they same. Frankly we are far from the same and I truly believe that feminism has not only given women a raw deal in general, but is also in the process of creating wimpy men also. This is one of the reasons why I am not really interested in an American woman. Many of them are what I call "half the man". I don't want my woman to be the same as me. But this topic is not about gender equality vs traditional family roles. The other side of the equality is likely not there either: financial. Although in some ways it is closer than many might believe. In the US especially now, there is less disposable income than there was 5 years ago. And so a trip from the western US to Ukraine or Russia may take quite some time to save for and also the vacation time allotted in the US is generally significantly lower than in Europe. Again, that is not the topic of this discussion.
To me I suppose that there are two categories of visits then that we may be talking about. The first is between two people who are more casual virtual acquaintances. In this case, it may be reasonable for the woman to pay for the trip abroad (or at least the travel expenses). I would not agree to pay for a woman I was not serious enough about or did not know well enough to fly here, but would be happy to entertain and such. However, if there is the plan for potential marriage then I think that the position I proposed earlier is the correct process: the man goes to the girl first and then ideally she comes to him temporarily. My experience is that the visit in her country (or a neutral site) is too much like a vacation and everyone has a good time on a vacation. Having the woman come for a month or more then is a chance to live as a couple in normal life where you are going to be living your life together. This is much more realistic opportunity to see if you are compatible truly.
I went through this same process a few years ago, met a nice girl on this site and after some time, visited her at her home, rented an apartment there and spent time together. Then a few months later, she came to the US for a week, although again this is like a vacation. At the end of last year, she came again for 2 months and we found that the situation was not as compatible as we thought and that was that.
But I paid for her trips here and mine there. She was not in a position to pay and I never expected her to do so. If she was my special girl, I would never have expected her to, that is my responsibility. But then I also think that much of this comes down to making a proper choice. You can spend a lot of money of you are not patient enough to spend the time. There is always a price of some sort.
As for women expecting me to pay for them, that is a different story. I have had women on this site want to meet immediately, to go away to some special vacation. This seems a bit pretentious to me and the sort of girl I am interested in would not suggest such beyond possibly asking when I would come to her to visit.
All that being said, if the man decides to offer a paid trip to him for the woman, that is matter between then, but I don't think I would do that myself.