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We perform a rigorous cosmology analysis on simulated Type Ia supernovae (SNe Ia) and evaluate the improvement from including photometric host galaxy redshifts compared to using only the “ z _spec ” subset with spectroscopic redshifts from the host or SN. We use the Deep Drilling Fields (∼50 deg ^2 ) from the Photometric LSST Astronomical Time-Series Classification Challenge ( PLAsTiCC ) in combination with a low- z sample based on Data Challenge2. The analysis includes light-curve fitting to standardize the SN brightness, a high-statistics simulation to obtain a bias-corrected Hubble diagram, a statistical+systematics covariance matrix including calibration and photo- z uncertainties, and cosmology fitting with a prior from the cosmic microwave background. Compared to using the z _spec subset, including events with SN+host photo- z results in (i) more precise distances for z > 0.5, (ii) a Hubble diagram that extends 0.3 further in redshift, and (iii) a 50% increase in the Dark Energy Task Force figure of merit (FoM) based on the w _0 w _a CDM model. Analyzing 25 simulated data samples, the average bias on w _0 and w _a is consistent with zero. The host photo- z systematic of 0.01 reduces FoM by only 2% because (i) most z < 0.5 events are in the z _spec subset, (ii) the combined SN+host photo- z has ×2 smaller bias, and (iii) the anticorrelation between fitted redshift and color self-corrects distance errors. To prepare for analyzing real data, the next SN Ia cosmology analysis with photo- z s should include non–SN Ia contamination and host galaxy misassociations.