Selective area growth (SAG) of nanowires and networks promise a route toward scalable electronics, photonics, and quantum devices based on III-V semiconductor materials. The potential of high-mobility SAG nanowires however is not yet fully realised, since interfacial roughness, misfit dislocations at the nanowire/substrate interface and nonuniform composition due to material intermixing all scatter electrons. Here, we explore SAG of highly lattice-mismatched InAs nanowires on insulating GaAs(001) substrates and address these key challenges. Atomically smooth nanowire/substrate interfaces are achieved with the use of atomic hydrogen (a-H) as an alternative to conventional thermal annealing for the native oxide removal. The problem of high lattice mismatch is addressed through an InxGa1-xAs buffer layer introduced between the InAs transport channel and the GaAs substrate. The Ga-In material intermixing observed in both the buffer layer and the channel is inhibited via careful tuning of the growth temperature. Performing scanning transmission electron microscopy and x-ray diffraction analysis along with low-temperature transport measurements we show that optimized In-rich buffer layers promote high-quality InAs transport channels with the field-effect electron mobility over 10 000 cm(2) V-1 s(-1). This is twice as high as for nonoptimized samples and among the highest reported for InAs selective area grown nanostructures.