A couple of points. Yes, the measurement microphone will affect the results and not just from the frequency response perspective, but also potentially from the polar and phase responses. For example, using a mic that is not perfectly omnidirectional at all frequencies could introduce non-linearities for any off-axis sounds.
Second, when making any measurements of system response you need to make them at several locations. Making things better at one location can make it worse at others.
Finally, measurement systems such as RTA, FFT, TDS, MLS or SIM are indeed just tools. They cannot tell you what sounds 'good' or 'right'. However, they can be very valuable in helping you see the problems, assesing what affect any changes made and determining what can or cannot be fixed via EQ. This last is where RTA systems have problems, they are indeed 'time blind' and display finite bandwidths so they are of limited use in assessing the causes of the problems and whether they can be addressed with EQ. Factors such as combfiltering, driver/speaker time alignment and room modes cannot be fixed with EQ and an RTA will not identify if what you are trying to fix is a basic frequency response issue or one of these issues than cannot be fixed with EQ.
RTAs are a great way to get some understanding of the relationships between frequency and sound and to identify gross problems such as feedback, but they will not keep you from spending hours trying to fix a problem that potentially cannot be addressed with EQ.
Second, when making any measurements of system response you need to make them at several locations. Making things better at one location can make it worse at others.
Finally, measurement systems such as RTA, FFT, TDS, MLS or SIM are indeed just tools. They cannot tell you what sounds 'good' or 'right'. However, they can be very valuable in helping you see the problems, assesing what affect any changes made and determining what can or cannot be fixed via EQ. This last is where RTA systems have problems, they are indeed 'time blind' and display finite bandwidths so they are of limited use in assessing the causes of the problems and whether they can be addressed with EQ. Factors such as combfiltering, driver/speaker time alignment and room modes cannot be fixed with EQ and an RTA will not identify if what you are trying to fix is a basic frequency response issue or one of these issues than cannot be fixed with EQ.
RTAs are a great way to get some understanding of the relationships between frequency and sound and to identify gross problems such as feedback, but they will not keep you from spending hours trying to fix a problem that potentially cannot be addressed with EQ.