Why would Federal invest more (which is needed to increase processing rate) just to match Quebec's intake? Absolutely no interconnection, unless Quebec Govt. requests Federal for a quicker processing and a formal alignment is obtained.
They are absolutely connected and bound to each other.
If you don't have CSQ you cant apply to Federal phase. Can you?
If Federal does not approve you, you can't get PR even though you have CSQ. Can you?
You can not separate these two processes. Because you need both of them to obtain PR. They are like key & lock.
Secondly, you asked why would invest Federal more on this? Because Quebec is in Canada and it is connected to Ottawa. Simple as is.
They are not an independent country, they tried twice but could not achieve. The federal government has responsibilities against every citizen, does not matter where they live, which is constituted by law. Furthermore, Quebec transfers billions of dollars tax payments to Federal each year, which makes Federal totally responsible for this case as well.