I have been able to replicate the same issue in ArcMap 10.7. I too could not assign a shortcut to the Make This the Only Selectable Layer command. Initially I thought this is one of those subversive changes ESRI have introduced in their attempt to phase out ArcMap. But I was able to create a CRTL+K for the Measure tool or even the Add Data button.
This made me think that there may be a set of commands that shortcuts simply don't work with. Think of this scenario you had successfully created a short cut to Make This the Only Selectable Layer but you have no layer selected in the TOC or you have multiple layers selected or even no layers in the TOC and then you go press the shortcut, what should happen? ArcMap blow up, fail gracefully or send an angry warning message? None of those happen when you use the tool as to use it you have to click on a layer.