Like Judaism and Christianity, Islam does not provide an explicit prohibition of Polygamy. Unlike Judaism, Christianity and perhaps-other religions as well, Islam deals with the issue more clearly and provides certain legal requirements and restraints that amount to the discouragement of such a practice.
The reason for not prohibiting polygamy categorically is perhaps due to the fact that there are certain conditions which face individuals and societies in different places and at different times, which make the limited practice of polygamy a better solution than either divorce or the hypocritical pretence of morality.
Out present day feelings about what is "tasteful" or "distasteful" are something we cannot force on all people everywhere, at all times and under all conditions, unless it is a question of a law coming God. This leads to the following question.