High amplifier open-loop gain is a good initial selection criterion for the highest accuracy circuits but isn’t enough by itself to guarantee the system will be linear to that extent. Open-loop gain is specified via a two-point measurement and doesn’t consider the non-linear uncertainty in open-loop gain at other operating points. MT-044 discusses open-loop gain uncertainty, how it translates into gain non-linearity and how it can be measured.
Other, possibly less obvious sources of amplifier non-linearity should also be considered. For example, source impedances can interact with non-linear input currents and cause non-linearity totally independent of open-loop gain. Also, uneven thermal heating of gain resistor networks can also cause significant non-linearity since the gain is changing as a function of the input and/or output signal levels.