In control theory, an accurate transfer function of the components of your system, and some sort of guarantee that they are independent (low output impedance and high input impedances) are important for understanding your system, if you want to model it accurately.
Sometimes, this can be simplified -- when the frequencies of interest are far below the GBP of the components used for example, the component can be approximated as a component with a single pole and a large DC gain, both of which can be pulled pretty easily from the datasheet.
However, when you are trying to eek out all the performance you can out of a component -- ie using an op amp with a GBP of 3MHz and you want to use all 3MHz -- then an accurate transfer function might be helpful.
How do you find such a transfer function? Can I just find all the points of the open loop Bode plot for an op amp and digitize it? It is easier if I understand where the poles and zeros are, are there any tools to take something like this and turn it into a transfer function? Is this done in "real life", or do people just work with approximations (or spice)?
As an aside, if this is something that is typically done, why don't manufacturers give the transfer function in the datasheet?