The Ghost in the (Time) Machine
The ubiquitous trope of the hero as mouthpiece for the author helps explain why so many Time Crashers travel in mind but not in body: the important thing is to bring the hero's knowledge and perspective. When bodies do travel, they are often accompanied by useful artifacts, particularly laptop computers (the material embodiment of information from the future). The series Save the USSR! (Spasti SSSR!) splits the difference: the adult hero's mind ends up in the body of his fourteen-year-old self, but has magically gained the power of "brain-surfing": he can call up any necessary information as if he had the entire Internet downloaded into his adolescent head.
On a superficial level, psychic time travel avoids some of the more obvious potentials for paradox. When Marty McFly meets his future parents in the 1950s in Back to the Future, that means that, as teenagers, they always knew someone who would happen to look like the teenage son they would have decades later. But the implantation of the adult mind into the child's or adolescent's body turns out to be fraught with perils not unlike Marty's near-incestuous encounter with his future mother.
Trying to fix world or national history by hijacking one's own personal history is the assertion of a particular type of cosmos, in which the micro is a synecdoche for the macro, like ontogeny recapitulating phylogeny. The personal is not just political; it is integral to the fate of the nation. This is narcissism on a cosmic scale, beyond even the "great man" theory of history. The hero/authorial stand-in (usually an office or IT worker, both of which are likely day jobs for F&SF writers) just happens to be the person who can save everything. Office plankton to the rescue!
He came from the past to change the future…
Psychic time travel lays bare the device of post-Soviet nostalgia and historical fandom: watching or reading stories of the Soviet past can be a form of escapism, sending the audience back to memories of an idealized time. The psychic Time Crasher moves the audience out of the role of passive spectator and into something more like the status of a gamer in a first-person shooter. These stories emplot the phenomenon Svetlana Boym calls "restorative nostalgia," which "reconstruct[s] emblems and rituals of home and homeland in an attempt to conquer and specialize time." In terms of fandom, these stories combine the "curatorial" ethos (guarding the canon against heresy) and the "transformational" impulse (in fixing history, the Time Crashers are improving on a beloved storyworld).
By necessity, psychic travel along one's personal timeline reduces the scope of time travel to the length of the hero's lifespan. Pensioners go back to World War II, while members of the last Soviet generations end up somewhere in the Brezhnev era. In each case, the connection between the personal and historical is far stronger than any jaunt to the age of Ivan the Terrible might be. The Soviet Union, we should recall, lasted for just under 74 years (if we count from the October Revolution), which was only a few years longer than the average Soviet male lifespan in 1991 (68.47 years). The USSR's lifecycle is easily comprehensible in human terms, all the more so for people whose lives began in the Soviet Union. In trying to correct the moments where their country went wrong, these Time Crashers are rebooting their own lives.