Bayesian hierarchical inference of phenomenological parametrized neutron star equations of state (EoS) from multiple gravitational wave observations of binary neutron star mergers is of fundamental importance in improving our understanding of neutron star structure, the general properties of matter at supra nuclear densities, and the strong nuclear force. However, such an analysis is computationally costly, as it is unable to reuse single-event EoS agnostic parameter estimation runs that are carried out regardless for generating gravitational wave transient catalogs. With the number of events expected to be observable during the fourth observing run (O4) of LIGO/Virgo/KAGRA, this problem can only be expected to worsen. We develop a novel and robust algorithm for rapid and computationally cheap hierarchical inference of parametrized EoS from gravitational wave data which reuses single-event EoS agnostic parameter estimation samples to significantly reduce computational cost. We efficiently include a priori knowledge of neutron star physics as Bayesian priors on the EoS parameters. The high speed and low computational cost of our method allow for efficient recomputation of EoS inference every time a new binary neutron star event is discovered or whenever new observations and theoretical discoveries change the prior on EoS parameters. We test our method on both real and simulated gravitational wave data to demonstrate its accuracy. We show that our computationally cheap method produces EoS constraints that are completely consistent with existing analysis for real data, the chosen fiducial EoS for simulated data. Armed with our fast analysis scheme, we also study the variability of EoS constraints with binary neutron star properties for sets of simulated events drawn in different signal-to-noise ratio and mass ranges.