We present the largest spectroscopic study of the host environments of Type Ibc supernovae (SN Ibc) discovered exclusively by untargeted SN searches. Past studies of SN Ibc host environments have been biased towards high-mass, high-metallicity galaxies by focusing on SNe discovered in galaxy-targeted SN searches. Our new observations more than double the total number of spectroscopic stellar population age and metallicity measurements published for untargeted SN Ibc host environments, and extend to a median redshift about twice as large as previous statistical studies (z = 0.04). For the 12 SNe Ib and 21 SNe Ic in our metallicity sample, we find median metallicities of log(O/H)+12 = 8.48 and 8.61, respectively, but determine that the discrepancy in the full distribution of metallicities is not statistically significant. This median difference would correspond to only a small difference in the mass loss via metal-line driven winds (<30%), suggesting this does not play the dominant role in distinguishing SN Ib and Ic progenitors. However, the median metallicity of the 7 broad-lined SN Ic (SN Ic-BL) in our sample is significantly lower, log(O/H)+12 = 8.34. The age of the young stellar population of SN Ic-BL host environments also seems to be lower than for SN Ib and Ic, but our age sample is small. A synthesis of SN Ibc host environment spectroscopy to date does not reveal a significant difference in SN Ib and Ic metallicities, but reinforces the significance of the lower metallicities for SN Ic-BL. This combined sample demonstrates that galaxy-targeted SN searches introduce a significant bias for studies seeking to infer the metallicity distribution of SN progenitors, and we identify and discuss other systematic effects that play smaller roles. We discuss the path forward for making progress on SN Ibc progenitor studies in the LSST era.