The senate may play an important role, but it still is made up of appointed members, while that may be suitable for the judiciary is it really consistent with a modern democracy.
As I see it we've come to the point where we invariably end up with PMs who see themselves as heads of state without the balancing effect of a seperate elected legislative body. The PM is part of Parliment and can often use that position to circumvent the checks and balances a more broad based democratic system offers.
If we're going to have PMs that act as Presidents then lets bring in the kind of system that will allow a healthy functioning of our government.
A system that gives MPs more power to hold the Pm and govt to account is good. We don't have that right now. The executive which is the PM, runs Parliament like a chess player moves his pawns on a chessboard. Our legislature is very weak in Ottawa as ut cannot subpeona information to do its job properly.