You would usually want the rose of the knob or handle to be in the middle of the stile (the vertical timber forming the side of the door), for symmetrical elegance. Yours are not wide enough
It is also possible to fit it in the horizontal rail, depending how the doors are made. Because the hole for the latch will weaken the tenon or dowels holding the door together.
Some doors, particularly modern fire doors, which are usually 44mm thick, are made of solid chipboard, moulded to shape and veneered, and these have no dowels or tenons, so can be drilled or morticed. These doors are flatteringly described as "engineered timber" which can also mean scraps of wood glued together.
The tubular latches I linked are fitted into a fairly small hole drilled in the edge of the door, so can usually be fitted.
To conceal the holes for the original handles, on veneered doors, you can use finger plates, often brass, but can be chrome, stainless, painted or ceramic. Painted doors can easily be filled and painted to hide holes