It well-known that the primary purpose of marriage is to begot children.
Since humans begets children through sexual reproduction. The role of men is very limited. He needs to contribute his tejas, which may take few minutes. But, the role of women is important and it takes atleast nine months. Mother's disposition can effect the child. So, it may be illogical to argue that both men and women are equal in all the aspects whenever married life is concerned. A men can give birth to large number of off-springs. But , comparatively a women can give birth to very less number of off-springs in her life time by means of natural reproduction. Similarly, there are several inherent differences in dharmas, genes, physical restrictions, capabilities etc.,
But, this question is only regarding the practice of Sati in scriptures.
If husband of a women dies, then she has multiple options: Sati, begetting children through niyoga, marrying husband's brother dharma are three among them. Along with the three mentioned, she can also spend the time at her own will like Satyavati, Satyabhama (as vanaprastha) etc., Niyoga and remarriage are banned in Kaliyuga.
Does any scripture prescribed any variant of Sati for men? If yes, what are those methods of leaving body after the departure of his wife? If no, is there any reason for not prescribing such an act for men?
This question has no yuga restrictions, if any variant of Sati is mentioned for men in any yuga, it is allowed to mention it.
Possible reasons I am thinking:
There is a restriction for grihastra man to beget children for clearing pitru-runa, which may not be mandatory for women. If it is a valid reason, then can he leave after begetting children if his wife departures?