We don't do it all the time because it is called a "hanging strop", not a "table strop".

No, seriously, do you have a table available in your bathroom? Most of us don't. A hanging strop is designed to be hung anywhere and save space doing so. Once attached to the wall or doorknob or towel rail or whatever, the hanging strop can remain there forever more.

In addition, as your stropping progresses you will find that varying the tautness of a hanging strop (by small degrees) can be a useful exercise on occasion - this is something that cannot be done on a paddle strop or a hanger lying on a table.

In fact, you might say that the hanging strop, of all the strop types, when used in its correct configuration is the strop equivalent of the straight razor in that you have complete control over ever aspect of it - angle in the vertical and horizontal planes, tautness etc. The other kinds of strops all have an inbuilt tautness or stability that to me marks them as the strop equivalent of safety razors.

James.