The CMHC isn't a constructor, they have no way of building houses themselves. They need to pay people to build it through their funding, except them providing funding comes with issues too.

I am a designer on a low-income apartment building being constructed by a non-profit organization in Niagara Region and it is 100% government funded (through CMHC I believe). The government took nearly 9 months to approve the funding after all the bids by constructors were received around April 2022 and given the rate of inflation at the time (and construction inflation was higher than the general rate) no subtrades held their price. The government refused to increase the funding to cover the extra cost due to inflation and as a result this building is being value engineered to high heaven and will probably be pretty terrible build quality.

What you're asking for is effectively a blank cheque for subtrades (and to an extent, designers... even if CMHC uses generic plans everywhere they need local professionals to take responsibility for the permitting process of each individual build, which includes regular inspections and reports) because none of these people trust that the government is competent enough to actually do it properly so they price high to account for fuck ups. (Ex. If CMHC handed me plans to be used I definitely would not blindly sign things off for the local AHJ and put my professional license at risk)