The political branch of the government does not control interest rates, nor have any say in them. The Prime Minister cannot raise or lower interest rates.
This is the same in most western democracies, as such things cannot be left to political control.
"The Bank of Canada is a special type of Crown corporation, owned by the federal government, but with considerable independence to carry out its responsibilities."
https://www.bankofcanada.ca/about
They also add: "The Governor and Senior Deputy Governor are appointed by the Bank's Board of Directors (with the approval of Cabinet), not by the federal government."
... and the BoD are appointed by cabinet.
Does the political branch make the decisions? No. But they choose the people that do!
This by no means implies any control over interest rates. At all.
People are appointed, and that's where political input ends. And those appointed stay appointed, are not chosen lightly, markets do not react well to poor choice.
By your metric, you'd think our Supreme court judges were puppets too. They aren't.
People may have political leanings, but understand, that is not the same as allowing input where it is not allowed.
The government cannot interfere with the judicial branch, nor with fiscal policy. To do so, renders it a banana republic, or dictatorship, any attempts would be disaster, for those appointed take this very seriously.
A core part of the job is to ignore ministers, the PMO, and so on.
It is entirely independent.
You don't need someone that will take in your input when you install people that are going to do what you want in the first place.
Look, I know it's fashionable to claim that everyone just ignores their roles via legislation (such as the bank of canada act), ignores change and what's happening in the world around them, to instead act as puppets, but that's just not how it works.
In the US supreme court judges almost always agree with whatever position is favoured by the party that appointed them, even if nominally independent.
For example: https://www.politifact.com/factchecks/2021/jun/23/trey-wingo...
That'd only be the case if there were no policies with bi-partisan support. How many of those 9-0 are for politically contentious issues?
And you're confusing political leanings, with influence. Political leanings which can, and have changed over careers. Not to mention, some of them outlive everyone who appointed them.
The Governor(not director) os not appointed by the government. Nor fired.
You need to read up on this. Please. You're just making stuff up.