Blended gases are best used where the required dispense pressure exceeds the dissolved CO2 level. For most beers in the US, the dissolved CO2 pressure is 12 to 15 psi. Beer left at full CO2 pressures above that will gain carbonation at the top of the keg and eventually become a foamy mess.
Blended gas has a portion that does not readily dissolve in beer (typically nitrogen) and displaces CO2, thus eliminating over carbonation. Lower carbonation beers (cask types and some Stouts) benefit from blended gas because the beer can't over carbonate. They might have the equivalent of 5 or 6 PSI in dissolved CO2, but the line requires 15 PSI to dispense.
Using a nitrogen faucet is not a requirement for these lower CO2 beers, but they sure do make 'em pretty.
So, you're on the right track. Indeed you do want to carbonate with straight CO2 according to a typical carbonation chart. Then you want to dispense with the mixed gas set for whatever your kegerator needs. On the other hand, if your dispense pressure and carbonation level are even, you want to use just straight CO2 because the blended gas will make your beer go flat as the differing CO2 levels even themselves out.