Some online have adopted the “Heartiste view” of sexual modernity, that a small number of men are slowly monopolizing access to most of the women. Heartiste himself was a great talent, but the people who imitate him are not; this was one of his blind spots. Statistically1, sexual inequality in the United States is rising:

…Within both sexes. But 100% of this effect is explained by the rise in virginity:

Height and attractiveness are very poor predictors of # of sexual partners in both sexes. Not because being tall and hot isn’t good, but because most tall and hot people would rather find one higher quality mate than multiple low quality ones.
Besides the Heartiste view, some think that polygamy is adaptive in the current environment. Regardless of whether this is the case, the West has been overhwelmingly monogamous for a long time, at least 2,000 years. This preference survived religious changes, massive economic shocks, the black death, wars, population increases, and changes in political systems. The only European religions who embraced polygamy are the Mormons and Muslims in the Balkans; both of which abandoned the practice. The only people left standing are FLDS deviants.
The elephant in the room here is genes. People’s sex drives and personalities determine how they interact with the opposite sex, traits with a substantial genetic component.
There are two ways that polygamy could be adopted in the first world. One is religious change: Christianity starts encouraging polygamy, or a new religion becomes popular which encourages polygamy. Something tells me that’s not going to happen.
The other is if the “polygamous phenotype” is genetically selected for and culture accordingly adapts. I see no evidence for polygamous behaviour being selected for:
Extraverted, agreeable, unconscientious, emotionally stable, and closed-minded individuals2 have higher fertility in the USA. Higher extraversion should lead to more polygamy, but this is balanced out by the increase in agreeableness and emotional stability.
On a genetic level, ADHD, smoking, BMI, and extraversion are being selected for in the UK; educational attainment, cognitive ability, height, and autism are being selected against. Higher rates of ADHD should lead to more polygamy, but this is balanced out by the fact that every psychiatric disorder except for ADHD is associated with lower levels of fertility:
from here
Self-reported sexual activity is of decent quality. Sometimes you have problems, like teenagers claiming to have a body count of 50, but usually people tell the truth.
Polygamy requires a very disruptive process where surplus males are gotten rid of.
The polygamous LDS factions expel a lot of teenage males for being disruptive. This works because they can be absorbed into a massive surrounding population of white Americans who are monogamous.
But I do not know how it would work at societal level.
Aside from my nit below, a few notes
1. Consideration of this question should engage with the issues of porn consumption and chatbot companions. My sense is that delayed loss of virginity is partly due to heavy porn consumption by young men. Inasmuch as this removes men from the active dating pool, it could _increase_ the extent of polygyny (and perhaps has contributed to its rise in the US). I'm unsure what to expect from chat companions other than less amory at all
2. Not that many people have to be polyamorous for it to have an effect on the experience of dating. I admittedly live in Berkeley, which is the epicenter of the polyamory movement, but it's impossible to date, or frankly go anywhere, without running into these people. Unlike normal young adults, who might be single and looking 1/4 of the time, they're just always on the market, and so heavily overrepresented. They also seem not to have the social sense to know when not to be on the prowl
3. Friends who are more sensitive to social currents than I am tell me that polyamory is becoming passé among the social vanguard. I haven't been able to discern this myself (cf Berkeley, above), but the polyamorous obviously incur a lot of drama, and it's easy to see how this could be self-limiting
4. imo the example of the LDS supports the notion that mating patterns are more culturally determined than biologically determined, and I don't think that we should weight Europe's history of monogamy too strongly here. It does seem clear that we've been in a period of rapid social change for the past 10+ years, and it's too soon to know how it will shake out