What I believe that you are saying is that for a nominal TIT (turbine inlet temp) the actual blade and vane temps may be much hotter due to reduced cooling air flow from the compressor.
This is not correct. While thermal damage can occur in the burner cans due to a hung start or introduction of fuel at too low a speed, the problem which occuring isn't fuel burning beyond the cans and causing thermal damage in the turbine wheels. When damage like that occurs, it's the introduction of too much fuel and fuel streaking (bad nozzles). In such cases where excess fuel is causing excess temperatures, it's going to show up as EGT or ITT/TIT. When the turbine wheels get hot, you're going to see it on the engine instrumentation.
Long cold starts aren't the problem. Long hot starts are. Hung starts are...which is part of the reason that most manufacturers put a five second cutoff for a hung start (or less).
The most fragile part of the engine, and the part that requires and uses the most air cooling and is most critical for air cooling, is the burner can. The burner is very thin. When I have handled them or removed them during hot section inspections, I have often seen them full of cracks; this is common due to thermald damage. A burner can is very thin, beer can thin, and very fragile. Holding one and turning it over in your hands sounds like a tinkling christmas tree ornament. The burner can employs vents and louvers to use airflow to keep the flame pattern off the burner can walls; the walls are actually protected by a layer of air during the start process and beyond. The majority of the airflow through the engine core is for cooling, not burning, and it's primary cooling duty is the burner can. It's the can that suffers the most damage during a hung start, but it's the after-components such as turbine wheels and the nozzle that suffer during a hot start.
The reason for having a minimum start RPM prior to introducing fuel is to protect the burner can, not the turbine wheels. While the turbine wheels can be damaged easily with excess temperature, operating at too low an RPM is a threat to the burner can first and foremost because it takes a minimum RPM to put enough air through the can to create a layer of insulating air inside the burner itself. Additionally, fuel doesn't atomize properly in the center of the can, leading to hot spotting and burning on the can itself, and the carriage of unburned fuel beyond..which can do spot damage to the turbine wheel(s).
Hung starts at higher RPM's, such as 35% (too high to be a max motoring speed for the starter alone) will be doing burner can damage if an excess or stalled EGT tempeature is seen, but more typically will see a stalled RPM with a rapidly climbing EGT. In this case, the threat is to both the burner can and the turbine wheels, stators, nozzle, etc.
An engine may certainly merit an inspection or even teardown following a hung start, depending on what has occured.
Start RPM's that are provided are minimum numbers, not maximum numbers with respect to motoring speeds.
A cooler start with a higher max motoring speed is NOT bad for the engine, and excess airflow beyond that provided at minimum motoring RPM does NOT harm the engine or it's components. A cool start is not the same as a hung start. A cool start is not detrimental to the engine, though too low a motoring speed certainly is. Regardless, you are NOT going to harm the engine or the starter by taking it to max motoring speed prior to introducing fuel and ignition.