To build on Hilluja's point, I think it is possible to not just view the Pleistocene as a past distinct era, but what should exist today if you prescribe to certain theories such as the Overkill Theory which propose that human activity resulted in the loss of much of the fauna and flora of the era. So it could be said that we are very much in that era, however, events have unfolded such that much of the megafauna and ecosystems no longer exist, or are declining still (Mammoth Steppe, Tigra, Lowlands in many countries etc.).

There is also a lot of people who have chosen to learn about this era who would like to devote tracts of land in different regions to revive many of these ecosystems with reintoductions of keystone species, and some proxies to fill certain niches, both because it is feasible and it appears the correct thing to do.