  Ratios of different ions of the same element encode ionization information
independently from relative abundances in quasar absorption line systems,
crucial for understanding the multiphase nature and origin of absorbing gas,
particularly at $z>6$ where H I cannot be observed. Observational
considerations have limited such studies to a small number of sightlines, with
most surveys at $z>6$ focused upon the statistical properties of individual
ions such as Mg II or C IV. Here we compare high- and low-ionization absorption
within 69 intervening systems at $z>5$, including 16 systems at $z>6$, from
Magellan/FIRE spectra of 47 quasars together with a Keck/HIRES spectrum of the
`ultraluminous' $z=6.3$ quasar SDSSJ010013.02+280225.8. The highest redshift
absorbers increasingly exhibit low-ionization species alone, consistent with
previous single-ion surveys that show the frequency of Mg II is unchanging with
redshift while C IV absorption drops markedly toward $z=6$. We detect no C IV
or Si IV in half of all metal-line absorbers at $z>5.7$, with stacks not
revealing any slightly weaker C IV just below our detection threshold, and most
of the other half have $N_\mathrm{CII}>N_\mathrm{CIV}$. In contrast, only 20\%
of absorbers at 5.0--5.7 lack high-ionization gas, and a search of 25 HIRES
sightlines at $z\sim3$ yielded zero such examples. We infer these
low-ionization high-redshift absorption systems may be analogous to metal-poor
Damped Lyman-$\alpha$ systems ($\sim1\%$ of the absorber population at
$z\sim3$), based on incidence rates and absolute and relative column densities.
Simple photoionization models suggest that circumgalactic matter at redshift
six has systematically lower chemical abundances and experiences a softer
ionizing background relative to redshift three.
