Private companies are woefully ineffective in this policy (this is also the historical truth of the Italian 110% tax credit on retrofits, that failed). They do what’s profitable for them, regardless of the stated objectives of the policy. In this case, they were (and continue to be) good at retrofitting single-standing houses for the rich and the upper middle class. The Priu coop is better at retrofitting the large buildings where (1) most people live, (2) most emissions are generated, (3) the cost per square meter of retrofitting is lowest. So they are more efficient because they do the job that the collectivity is paying for (via taxes) instead of what is good for their (singular) bottom line.
It is false that coops have no incentive to grow (though Friedman believed it). Our main econ sci-fi element is the creation of a new economic actor, a “mutant”: quintuple bottom line companies. Priu wants to grow, because it can hire more people (doing well on the “people” bottom line), and fund art and beauty (on the “beauty” bottom line, etc.). It just does not want to grow only on the surplus side. It does want to grow its surplus, unless it clashes with other dimensions of its bottom line: for example, real-world worker coops do not fire their members to offshore production. Quintuple bottom line coops would also refrain from growing if that would impact planet, beauty or truth.
Fraud happened in the (real) 110% story. Priu itself has really no incentive to commit fraud, because of the reputational consequences associated to the dense web of relationship between actors.