It is discriminatory as it treats them differently from a person coming out of a divorce or separatation, where the CSA enforces support for the children, even when a new relationship is established.
It represents a financial penalty on the widow/widower and a burden on the new partner, which leads to many widows being forced to maintain a sole parent existence. Effectively it represents an expectation on the part of the state that a new partner should take financial responsibility for children that are not theirs, whilst they are likely to have existing responsibility still for their own.
The benefits of supporting new relationships financially through maintaining widow/widower pensions are many. It would encourage a two-parent environment, with the obvious advantages to both children and adults. It would provide benefits in terms of the reduced need for housing, environmental benefits through savings in energy and security benefits through mothers not having to live on their own.