Closed loop vs. open loop system analysis and design
Open loop analysis (bode/Nyquist) is carried out out on the open loop because the stability margins can be measured, adjusted and set. If the stability margins (and encirclements of the -1 point) are adequate for the open loop then the system should be unconditionally stable when the loop is subsequently closed.

Both Bode and Nyquist are frequency response analysis techniques. The loop is opened, a signal is injected into the break and the phase &amp; magnitude measured at the output of the loop over a range of input frequencies. When this is done it is the complete loop that is included in the measurements including the feedback transfer function. This would be called measuring the "loop" phase and magnitude as opposed to the "open loop" which usually refers to just the forward part of the loop.

Root-Locus analyses the closed loop transfer function by plotting the closed loop poles as some system parameter is varied from 0 to infinity. The parameter to be varied would normally be the open loop DC gain, K. Using this technique the value of K can be determined for a desired stability or damping factor.

Measuring closed loop gain and phase won't give you a measure of how close to instability the closed loop system is, where as open loop analysis allows the designer to set gain margin and phase margin for the desired amount of system stability.