Fast radio bursts (FRBs) are short-duration radio transients that occur at random times in host galaxies distributed all over the sky. Large field of view instruments can play a critical role in the blind search for rare FRBs. We present a concept for an all-sky FRB monitor using a compact all-sky phased array (CASPA), which can efficiently achieve an extremely large field of view of $\sim10^4$ square degrees. Such a system would allow us to conduct a continuous, blind FRB search covering the entire southern sky. Using the measured FRB luminosity function, we investigate the detection rate for this all-sky phased array and compare the result to a number of other proposed large field-of-view instruments. We predict a rate of a few FRB detections per week and determine the dispersion measure and redshift distributions of these detectable FRBs. This instrument is optimal for detecting FRBs in the nearby Universe and for extending the high-end of the FRB luminosity function through finding ultraluminous events. Additionally, this instrument can be used to shadow the new gravitational-wave observing runs, detect high-energy events triggered from Galactic magnetars and search for other bright, but currently unknown transient signals.