The HP 200LX and similar used a 186-compatible CPU called "Hornet". Using an actual 80186 in a PC compatible would have been damn near impossible; the 186 was a system-on-chip design that had built-in timers, an interrupt controller, and other gubbins. Some of these were mapped to devices that had other devices mapped to them in the PC design, so building a 186-based system that met the common threshold for PC compatibility (i.e. it ran the IBM versions of Lotus and Flight Simulator acceptably well) was a nearly insurmountable task.

Because it acted more like a real OS, with user programs calling through driver APIs rather than touching the hardware directly, with the right driver support Windows could run on a 186-based system; one (the Tandy 2000) was used to develop Windows 1.0's color modes because it had a high-resolution 8-color display before the EGA came out: https://www.1000bit.it/lista/t/tandy/tandy2000_ad.jpg

ISA-compatible "clones" of the 186, like the NEC V40 and the "Hornet", did not have the SoC problem and could be used in PC-compatible system designs.