This is a fairly broad question that depends to some extent on the countries you're comparing the US to.

At it's heart, separatist movements tend to be founded on a regional culture/subculture being different to the ruling culture, and feeling that their regional people would be better off independent than as one piece of a larger empire.

Russia and China have separatist movements, but in the past they've absorbed other peoples and regions during times of expansion. Those individual conquered peoples maintain substantial regional populations, difference in policy opinion than the occupying country, and different culture than Russians/Chinese.

The closest parallel for the US would be the native Americans. They certainly have their own separate cultures, but they've been left with diminished populations through centuries of disease and skirmishes. Furthermore, the individual tribes had difficulty putting together a united front, leaving any one group too weak to seriously consider it. Furthermore, decades of powerful and loud American culture has helped to assimilate and homogenize the populace, establishing shared values, experiences, and concerns.

One thing that does make former colonies more unified than old world countries is the act of colonization, and it's demonstrated linguistically.

Take Britain and the US. There are thousands of different individual regional dialects across the British isles, to the point that a skilled linguist can pinpoint where someone grew up to within a few miles. When people came from Britain to the US, wherever the colonists came from, they ended up in the same coastal cities. These new colonies were melting pots, if not racially (still a bunch of white Englishmen), then linguistically. Eventually this melting pot would simmer down to favor the dominant dialect of the regions that contributed the most colonists. This homogenizing effect would only grow stronger as intermarriage became common, so that any one American could trace their lineage to a dozen places in Europe.

In effect, colonization was a "reset button" that erased many of the tiny regional cultural differences that had existed for thousands of years in the old world. There were still some regional variations between the individual colonies that stemmed mostly from economic considerations. Southern plantations needed manpower. Slavery was the cheapest source of labor. That one difference would go on to shape the regional culture into one slightly different than that of the north, and was enough to trigger the civil war.

In the US's case in particular, I'd also argue that especially in modern times, you have the consideration of "would our regional population be better off on our own than as part of the US?" The answer is typically no. Secession would mean losing many of the economic advantages the US provides, and it's not like the US has a particularly exclusionary or abusive government.

At the same time, though, that doesn't really get rid of the roots of separatist thinking. Texas has had people propose secession, the southeast has done it once before, and there are regional complaints about federal land use in the west that are similar to secessionist complaints.

I feel like I may be skirting the rules without having any cited sources, just my observations. But... If we are to look at Canada first, the main secessionist movement is based in the province of Quebec. Quebec is the only majority francophone province with a distinct culture from the rest of Canada. With Russia, most breakaway movements are based around ethnic and religious groups (Chechnya, Dagestan). Same thing with China, you have the majority Han people then separate groups like the Uyghurs and the Tibetans. Further, most of those groups are more or less confined within borders that reflect the extent of the group.

In the US however, historically, the only large ethnic group after Whites were the Blacks, but they were spread over a number of southern states and not in its own region. This, coupled with a lack of national identity as "black" rather than as "american" also diminished the chances of black separatism beyond your classic cases of the Nation of Islam and other similar organizations.

Also, since the US is an immigrant nation, people usually give up their previous identity in favor of being an "american," though some could argue that that is changing.