You're probably wrong in that assumption and I'll explain why.
1. Parliamentary systems don't have the same 2-party "big tent" approach as the US.
2. MP's don't raise their own war chests in Canada and don't have the same degree of "fuck you!" independence as in the US.
3. Political careerism in Canada is based on pleasing those in control of your party, not on direct access to the media and fund-raising.
4. The major parties in Canada have somewhat similar economic policies in any event.
5. Canada is a pragmatic country and is not as ideological as the US. There is a premium placed on consensus and "working together to get the job done". Doesn't exist these days in the US.
I think these are excellent points of difference. I still think there is a lot of sausage being made behind the scenes that give you a false sense of comfort. Why would Winston Churchill feel compelled to say “Democracy is the worst system, except for all the other systems”?
If the U.S. had a parliamentary system, it is most likely BBB wouldn't have even come forward. That's the biggest part of this. This would have all been debated at a closed door party session. Justin Trudeau and Boris Johnson don't craft legislation in a vacuum and roll it out for for a vote in Parliament. They have to balance the factions in their own party.
I'm not sure I want all this consensus. It seems artificial at times. A few years back, I cited an article that criticized Chancellor Merkel's ability to maintain control by co-opting the positions of the Social Democrats when it was convenient. The Germans had consensus, but not a robust competition of ideas. They had a Chancellor who held on to power for 16 years. That might seem like political nirvana, but Americans wouldn't want that system. I believe the U.K. Parliament has far more contention than Canada. These things go through cycles.
I think a lot of us down admire Senators like Manchin and McCain who buck their party's leaders. I'm sure someone here has commented on the media hypocrisy where Manchin is a goat, but McCain was a hero when he stood up to the party.