There are several workarounds that use only map algebra. A convenient one is to compute the flow accumulation for a constant map. Use a value of 1 to accumulate left to right and 64 to accumulate bottom to top. This effectively gives you $$ColMap and $$RowMap (indexing begins at 0). Adding 1/2, multiplying by the cellsize, and adding the origin recreates $$XMap and $$YMap. It's reasonably fast and not difficult to remember.
As a worked example let the origin be at (-500000, 0) and the cellsize be 10. Then
xmap = (FlowAccumulation(1) + 0.5)*10 - 500000Doing this in an unprojected coordinate system of course produces grids of longitude and latitude, respectively. Projecting the latitude grid (ymap) answers the question that started this thread. Note that the original elevation grid is used only to determine the extent, cellsize, and projection of the final grid; of course its values are useless.
ymap = (FlowAccumulation(64) + 0.5)*10