MoO3 is a wide bandgap (> 2.7eV) n-type material. Even IGZO falls under the same category (BG > 3.4eV). Still, why MoO3 is not used as a channel material in general? In most reviews/articles its mentioned that MoO3 has a wide bandgap, and its thermal emission is less to operate FET. Whereas IGZO has a much wider gap, still we can find plenty of FETs based on IGZO.
However, I found one paper where MoO3 is used after modifying its BG. (DOI: 10.1002/adma.201203346)
Withanage, Sajeevi S., Hirokjyoti Kalita, Hee-Suk Chung, Tania Roy, Yeonwoong Jung, and Saiful I. Khondaker. "Uniform Vapor-Pressure-Based Chemical Vapor Deposition Growth of MoS2 Using MoO3 Thin Film as a Precursor for Coevaporation." ACS omega 3, no. 12 (2018): 18943-18949.
I think there are not simple answer in this question. Commercially useful FETs should satisfy many conditions such as sufficient carrier concentration, adequate relation between the Fermi level position and conduction (valence) bands and dielectric constant for vertical electric field, also with electron affinity and work function for alignment with electrode to transport carrier well. In this regard, you can find the difference between IGZO and MoO3.
However, anyway if you want to see the operation of MoO3 FET, lots of oxygen vacancy in MoO3 can show FET operation with poor mobility, which is result of forming wide spread energy states in band gap.
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