I'm not sure it would accomplish much. There is provincial research funding, as you know, although at different levels across provinces, and it's not the lion's share of the research.
Traditionally, research has been a federal responsibility. In the United States, it's the same. I don't know what shifting it to the provinces would do practically in improving outcomes or excellence, etc.
I will say that the provinces work collaboratively with the federal government in shaping the system. They are the ones shaping the institution, shaping the enrolment corridors and regulating the post-secondary institutions across the country, so I think they have a bearing in how things get shaped.