Nothing logical or consistent about using the temperature of a fever and the ice/brine point in a lab as the basis of temperature measurement. The freezing and boiling point of water (at about sea level) are far more familiar to folks, and more consistent.
Interestingly, American Customary Units have been based on the metric system since the 1893 Mendenhall Order.
Why is it not logical? It was what he had to work with 300+ years ago, and in particular the temperature of ice and brine is as repeatable as freezing and boiling at a lab anywhere in the world.
"Based on" isn't correct terminology. US customary units are, by agreed convention, defined in terms of SI units(not metric units). In science in general, and in metrology specifically definition has a very specific meaning-it's an exact mathematical relationship.
We can carry that out even further and some definitions get really convoluted as units now are defined in terms of fundamental constants of nature, the values of which have been agreed up. An inch is exactly 2.54cm. 1cm is exactly 1/100 of a meter. A meter is the distance monochromatic light with a wavelength of 632.99121258µm travels in a vacuum in 1/299792458 seconds. The speed of light is exactly(by definition) 299792458 m/s. One second is defined as 9,192,631,770 transitions of a ground state Cesium-133 atom.
BTW, the celcius/kelvin scale has not bee defined in terms of the freezing/boiling point of water for a long time. It's the triple point of water.
Fundamentally ALL units of measure are arbitrary, and all have a logical basis. Imperial and US customary units were largely based on objects at hand...and incidentally the width of your hand is typically 1/3 the length of your foot, or 4" for a typical adult man.
As a point of annoyance for me, I'll also point out that the Metric system is NOT the measurement system used in science. Many metric units are used in science, but science long ago moved past the metric system.