WI: Alternate arrangement for Westminster-style democracies more widespread?

And by that alternate arrangement, I mean thus (composite of two Wiki articles):

Worthy of note is the fact that the governing party had chosen to sit on the left side of the House of Assembly as opposed to the traditional right side of the speaker. This tradition dates back to the 1850s because the heaters in the Colonial Building were located on the left side, and it was the warmest part of the house. Thus, the government chose to sit in the heat, and leave the opposition sitting in the cold. To this day the ruling party of the Newfoundland and Labrador House of Assembly continue to sit on the left side of the speaker of the house.

So, how could this arrangement be more widespread, particularly amongst British colonies?
 
"If you can't stand the heat get out of the kitchen!"
"This economic downturn is what happens when Her Majesty's Government leaves the Republican Party out in the cold."
 
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