  We present final statistics from a survey for intervening MgII absorption
towards 100 quasars with emission redshifts between $z=3.55$ and $z=7.08$.
Using infrared spectra from Magellan/FIRE, we detect 279 cosmological MgII
absorbers, and confirm that the incidence rate of $W_r>0.3 \AA$ MgII absorption
per comoving path length does not evolve measurably between $z=0.25$ and $z=7$.
This is consistent with our detection of seven new MgII systems at $z>6$, a
redshift range that was not covered in prior searches. Restricting to
relatively strong MgII systems ($W_r>1$\AA), there is significant evidence for
redshift evolution. These systems roughly double in number density between
$z=0$ and $z=2$-$3$, but decline by an order of magnitude from this peak by
$z\sim 6$. This evolution mirrors that of the global star formation rate
density, which could reflect a connection between star formation feedback and
strong MgII absorbers. We compared our results to the Illustris cosmological
simulation at $z=2$-$4$ by assigning absorption to catalogued dark-matter halos
and by direct extraction of spectra from the simulation volume. To reproduce
our results using the halo catalogs, we require circumgalactic (CGM) MgII
envelopes within halos of progressively smaller mass at earlier times. This
occurs naturally if we define the lower integration cutoff using SFR rather
than mass. MgII profiles calculated directly from the Illustris volume yield
far too few strong absorbers. We argue that this arises from unresolved phase
space structure of CGM gas, particularly from turbulent velocities on sub-mesh
scales. The presence of CGM MgII at $z>6$-- just $\sim 250$ Myr after the
reionization redshift implied by Planck--suggests that enrichment of intra-halo
gas may have begun before the presumed host galaxies' stellar populations were
mature and dynamically relaxed. [abridged]
