As a former soldier that taught several BMQs, reserve and regular force, I will chime in with my 2 cents.
I do see the value of common training syllabus and and having what appears to efficiency of training at a centralized school. However I have also seen the negatives. I remember in 2006-2008, St Jean couldn't keep up with recruiting and many Reg F BMQs were farmed out to Borden, Meaford and from what I heard Wainwright as well. I had first hand experience with the Meaford courses.
The ARes I think shows the way ahead. They do BMQ in like every possible location where there is an armoury. They have to. You don't want to drive recruits four hours just to do a course as one big happy family. It will suck resources.
So we know the army can do decentralized BMQ with so far good results, and have been doing it for many decades.
We have Navy, Army and Air Force Schools for trades training. Why not close down St Jean and add a few more PY to the appointed schools within each element (How many schools does Borden have?)
Its more important to have the correct syllabus in say the first (common phase?) of each environmental course. Its far more cost efficient to have a few trained SMEs that could then guide the course instructors in my view. The SMEs could be controlled by one CoE via email, zoom, etc.
In my view, the common phase on recruit training should be as follows (take 4-5 weeks)
-Military Knowledge
-C7 Service Rifle
-I feel 9mm pistol should be there too but thats another debate
-Drill
-First AId
-CRBN Defence
Thats it. Those are the common skills I think every serving member needs (less padres). But I am a retired WO who talks to cattle and sheep all day. So take it for what it is worth.