We need a term that specifies what situation we have. This is probably not a man that has divorced a wife, or outlived a wife. This is a man that has two wives. This is not legal in western countries, so we have this term "taken" to tell the whole story in a single word.

Taking second wife or another wife

You can't marry a wife. You marry a women, then she becomes your wife. If he marries another wife, well, that sounds funny. You take a wife = you get married

The phrase "take a wife" refers to getting married. When people marry in America, it is common for the person performing the marriage to say it to each person. For instance, suppose Jack and Jill are getting married. The person performing the wedding ceremony will often say the following, or something similar: "Do you, Jack, take Jill to be your lawfully wedded wife, to have and to hold, in sickness and in health, for richer or for poorer, till death do you part?" (Jack says "I do.") "Do you, Jill, take Jack to be your lawfully wedded husband, to have and to hold, in sickness and in health, for richer or for poorer, till death do you part?" (Jill says "I do.") Both sentences mean "Do you agree that... ...this person will be your husband/wife? ...that they will be yours? ...that you will love/care for them whether they are healthy or sick, and whether they are rich or poor? ...that this will continue until you or they die? Unless it is during the wedding ceremony, it is not common in spoken English to say that someone "took a wife." Most people just say that "they married." The phrase is far more common in written English, particularly in literature.