Why is Canada divided in much larger political sections than the US?

Part of what you’re seeing is improvements in transportation technology as well. If you have to rely on barges or sail or rudimentary roads, it limits the geographic area you can effectively govern; once the railroads start getting built, it allows the government to have a larger reach. You can see this in the size of the counties, too; as an example, Kentucky has over twice as many counties as California does despite being less than one-fourth its geographic size.

On the other hand, Kentucky used to be a county of Virginia… the time period of the very least developed transport was also the time of the very largest counties. And, to bring it back to Canada, the least developed sections there are the biggest, at least as a rough generalization.

Actually, they apparently thought that Alberta and Saskatchewan would be only one province, or at least, the inhabitants of Lloydminster, Alberta/Saskatchewan did:

There were proposals to admit the Prairies as one single province; it was actually the preferred option of the premier of the Northwest Territories at the time. Ultimately the decision to split the Prairies in two following a meridian fell down to the federal government.

Although the Prairies were split in a different way (as districts of the Northwest Territories) before provincehood.