Right now the mass of the kilogram prototype is defined to be exactly 1 kg. If someone adds or removes matter from the prototype, then the numerical value we assign to the mass of everything else in the world would change, but the prototype would remain 1 kg. On the other hand, currently, the value of Planck's constant is known only to a certain level of accuracy.
Under the new system, Planck's constant would be defined to be exactly 6.626070040e−34 kg.m^2.s^-1, with no error bars, and the prototype would no longer be exactly 1 kg. If we refine our estimate for the physical value of Planck's constant, its numerical value of 6.626070040e−34 kg.m^2.s^-1 would not change, but the numerical value for everything's mass would.
This definition of 1 kg requires we first define 1 m and 1 s, but there are already good definitions for these quantities based on fundamental physical properties (namely, the speed of light and the frequency of the transition between the two hyperfine levels of ground state of the caesium-133 atom).
Because in order to measure something in terms of a constant, you cancel out all the other units except the one you're measuring.
I.e., if you know how to measure a second, you could define the meter based on the speed of light by creating light in a vacuum and timing it.
Meanwhile, you can't define a meter or a second in terms of pi, because it has no units. It's just a ratio of the surface area of certain classes of object or shape to thheir dimensions.
The same way a measurement in the units of m/s (i.e. The speed of light) can be used to define the meter, given the second is defined via another method.
Under the new system, Planck's constant would be defined to be exactly 6.626070040e−34 kg.m^2.s^-1, with no error bars, and the prototype would no longer be exactly 1 kg. If we refine our estimate for the physical value of Planck's constant, its numerical value of 6.626070040e−34 kg.m^2.s^-1 would not change, but the numerical value for everything's mass would.
This definition of 1 kg requires we first define 1 m and 1 s, but there are already good definitions for these quantities based on fundamental physical properties (namely, the speed of light and the frequency of the transition between the two hyperfine levels of ground state of the caesium-133 atom).