In my opinion, one of the issues of the reform you are discussing is the change in political culture. If you can change that to get away from the excessive confrontation and blind partisanship that we have now, everyone would thank you for it and would benefit from that shift.
The British parliamentary system emerged in response to the monarch's abuse of power, which constituted absolute rule over the country for centuries. The monarch became a kind of figurehead and ceded his powers to the prime minister, which he no longer appointed because the prime minister was from then on the leader of the party that obtained the most seats in the House. So a political system developed that was still a monarchy, but it was an elective monarchy.
Is it not an abuse of power for people who do not even have the legitimacy of having been elected by the whole population to govern with a minority of popular support while using mechanisms such as closure to abruptly end debate and push through bills?