I was assuming that a purifier with RO stage will have a pump built in to generate necessary pressure. You cannot rely on the pressure generated from running taps. In fact, I used a Aquagard UV Purifier at the last place I stayed and the pressure in tap was rarely good for us, so I had to have a external pump installed.
I was looking for a tap less setup because taps run dry in summer and we should have a way to purify water directly.