Sounds like it’s simply an engineering issue that nobody has bothered to solve. You could 100% design a window unit that would fit a hinged window. But no company has bothered to do so.

You could always do a heat pump mini-split system instead. Those only require a single hole drilled to the exterior, which then gets used to run hoses into the house from the head unit. The whole thing can usually be installed in a few hours, because it’s basically “drill hole, bolt everything down where it needs to go, run hoses and power, seal hole with expanding foam”