All of the imposters you mentioned were impersonating people who died or disappeared from public sight, but would have had a strong if not definite claim to the throne. Similar instances are recorded in several countries histories. (Ex: Perkin Warbeck, the many pretend dauphins of France after the revolution).

Each of these impersonators with the exception of the Anastasias, was involved in attempting to gain power.

The Dmitrys all happened during the “time of Troubles”, which was a crisis of succession to the throne that was pretty brutal that lasted from 1598 to 1613. In the case of the false first Dimtry he even managed to snag the throne for a short while with the support of Polish and Lithuanian nobles and the Cossacks before being pushed out and executed less than a year into his reign. The second and third both followed suit after, but neither managed to claim the throne.

The Peter III impersonator was a Cossack soldier who apparently resembled the dead Tsar. He again was able to mobilize the disenfranchised Cossacks who felt they were being oppressed. He was pretty successful drumming up support until he started to get sloppy and eventually was turned over to the government.

The impersonators of Anastasia, Alexei, Olga, Tatiana, and Maria didn’t have a throne to claim, but several have written books or tried to capitalize on the fame in various ways. The allure of their story seems to lie in the secrecy of their deaths. It wasn’t even until 1991 that there was even for solid proof that they imperial family was executed back in 1918. Even then the final two bodies were only DNA tested in the early 2000s.

Can’t speak to the motives of the impersonators beyond just being people who saw an opportunity in times of upheaval and took advantage.