By abolishing this rule it would reduce bureaucracy and administration; reduce the effort required to investigate people's personal lives (a violation of their right to privacy – exemplified in the unfortunate situation that David Laws found himself in recently); and treat everyone as an individual.
Also this would actually be an incentive for people to live together; build more stable committed relationships rather than driving people apart for reasons of finance. They would benefit from pooling their individual resources.
This current system penalizes hard working couples who have the misfortune of one of them losing a job only to find that they are penalised for being in a relationship. They should not be penalised even more for the "offence" of being in a relationship.
Most importantly however the government should not be making decisions on my rights to benefits on who I choose to sleep with. My sex life should remain private and not an issue for taxation or benefit.
Benefit fraud would be easier to investigate if it wasn't required to spy on someone's love life as well. Also by focussing energies onto whether someone is actually looking for work it is much easier to make rulings on their right to Jobseekers allowance.