Molecular motors such as kinesin-1 work in small teams to actively shuttle cargos in cells, for example in polarized transport in axons. Here, we examined the potential regulatory role of the nucleotide state of tubulin on the run length of cargos carried by multiple kinesin motors, using an optical trapping-based in vitro assay. Based on a previous report that kinesin binds preferentially to GTP-tubulin-rich microtubules, we anticipated that multiple-kinesin cargos would run substantially greater distances along GMPCPP microtubules than along GDP microtubules. Surprisingly, we did not uncover any significant differences in run length between microtubule types. A combination of single-molecule experiments, comparison with previous theory, and classic microtubule affinity pulldown assays revealed that native kinesin-1 does not bind preferentially to GTP-tubulin-rich microtubules. The apparent discrepancy between our observations and the previous report likely reflects differences in post-translational modifications between the native motors used here and the recombinant motors examined previously. Future investigations will help shed light on the interplay between the motor's post-translational modification and the microtubule's nucleotide-binding state for transport regulation in vivo.