The underlying reason is that we don't actually need a unit for temperature. The temperature of a substance is simply the mean kinetic energy of its molecules which can be given in Joule. The problem is that historically thermometers were calibrated using the triple point of water and not by measuring the kinetic energy of the molecules. This is how the Kelvin scale used to be defined. The Boltzmann constant was simply a measure of the triple point of water in energy units (which could be measured). One problem was that the isotopic composition of water influences the triple point and was not well defined in the old SI system. Nowadays, we can actually calibrate thermometers by measuring the kinetic energy of molecules, so we no longer need to use the triple point of water. This is why the Kelvin is now just a rescaling of the Joule with a fixed coefficient (the defined Boltzmann constant). So the Boltzmann constant can no longer be measured. On the other hand, it is now possible to measure the triple point of water in Kelvin (this used to be 273.16 K by definition in the old SI system).

Not in SI. Kelvin is defined in terms of k_B. Joule is defined in several ways, eg force & distance.