IMHO making the QUEEN the absolute ruler is a better idea than giving Parliament that much power!!
Remember that under the UK's parliamentary system, the majority in Parliament selects the PM in the first place. They select him and they can remove him by a vote of "no confidence". Unlike the US system where the people elect (albeit indirectly via the electoral college) the President. The founders of the US felt that splitting power to declare war from that to make war, between Congress and the President, was wise, but in the UK Parliament has in effect both legislative and executive power.
In a way, this shift would change little.