Lamaism and polygamy probably might have entered into Bhutanese soil at the same time. There is no written record of Polygamy before propagation of Buddhism in Bhutan. The credit goes to Guru Rinpche (Precious Teacher) for propagating Buddhism in Bhutan around 746AD. It was Nyingmapa (old/ancient) sect of Buddhism which actually was tantric in nature.
Through out the legend and history especially in Buddhist hagiography, the kings and emperors were considered rich if he had many consorts, concubines and mistresses. Even thousand Buddhas were said to be sons of one king once in previous eon and Chana Dorji was said to be thousand and oneth in buddhist Namthars and hagiography.In one way, one could say that polygamy for temporal ruler were almost celebrated wealth and acceptable though it was obscure for disciplined Budhist practioners especially in acient India.
In Bhutan, polygamy by prominent Buddhist teachers started with visitation of Guru Padmasambhava. Guru Rinpoche was invited to Bhutan by King Sindhu Raja of Bumthang to cure his incurable illness. It was said that Sindhu Raja was king of Indian origin who fled India and settled in Bumthang Chakhar Dzong ( nine storey fortress). During invasion of Naoche, a rival king from Duars, Sindhu Raja sent his son Tagla Mebar to war. Before the war, king made offering to local deity Shelging Karpo invoking its power to protect his son and army in the war. However, his son was killed by Nachoe’s force. King in anger and desperation desecrated deity’s abode. It is believed thence, he became sick as deity had stolen his life force (rSog). No doctor could cure him and had to invite Guru himself.
Guru who already had few consorts and two main consorts like Mendarawa and Yeshi Tshogyel visited Bhutan. To lure Shelging Karpo to come out of cave, Guru made king’s daughter Trashi Khyeuden to carry water in the vase. After subduing of deity, King offered his teenage daughter as gift to Guru Rinpoche. Trashi Khyeuden was believed to be re-incarnation of one dakini, though one could agree that every consort of imminent Buddhist teachers were believed to having sign of dakinis. The arrival of Guru Rinpoche thus was arrival of both religion and lamaic polygamy.
Although Guru Rinpoche used to have many consorts, his was more of namesake and for wellbeing of individuals or sentient beings. Guru, though might have many consort, he didn’t leave behind his legacy or descendant. However, the need for polygamy in later period was more than religious.
In later period many Tibetan Lama came to Bhutan propagating Buddhist religion as well as spreading biological seeds. They went back with alms and left behind their love child. Still in later period, Lama like Phajo Drugom and Drukpa Kinely took numerous consort claiming that pretty girl posessed sign of Dakinis and were destined to be his mistress or wife thus providing him sons. For Drukpa Kinley, it was way of his teachings and he never used his illegal children to consolidate his power and leave behind his legacy.
But Phajo’s case was different. He used polygamy deliberately to enhance religiously, politically and socially. He made social connection through polygamy. He used his son to rule the regions he got from devotees. He used his son to consolidate Drukpa religion and his power, so that Lam Khanga never waged war again. Out of this polygamy, people were educated, preached and taught goodness. Still Polygamy is polygamy and in Bhutan polygamy, in my view, first introduced by Buddhist Scholar.