Thank you for your question.
The literature clearly shows that putting less emphasis on the identity of applicants leads to greater equality in outcomes. So the answer to your question is yes, we should be looking at that. Canada is doing very well, by the way. According to a study by Holly Witteman, a professor at Laval University, when the Canadian Institutes of Health Research decided to reduce the importance of résumés during the assessment of applications and give more weight to the actual project, there was no more gender inequality in the success rates. One could surmise that this will also reduce the weighted advantage of the more prestigious universities compared to the others.
I am therefore entirely in favour of anonymizing projects as much as possible, or, in the case of funding for professors, giving more weight to projects and less to applicants' résumés.