Different op-amps are better suited for different purposes. Op-amp rollers often use op-amps in circuit situations that they are NOT optimized for. In some of these situations, the op-amps may be ringing or even oscillating at very high frequencies.
An op-amp roller should have a high frequency (30 MHz or higher) O-scope, to check their work.
It is very critical, especially if designing ones own op-amp, to make sure that the input impedance -- and the VARIATIONS in input impedance are considered. For critical AC amplifier situations (audio is one such example), the balance and consistency of the input impedance can cause interesting distortion issues. JFET inputs do not solve all of the problems, but can help in certain cases -- big, fat low noise JFETs often have serious problems with capacitance, and that capacitance is not constant vs. the state of the component. That is one reason why a slightly smaller JFET with slightly worse noise specs might be A LOT better in a general purpose audio situation, and might actually manifest lower in-circuit noise than the bigger, fatter JFET that seems to have lower noise by superficial specs. Op-amp design is truly interesting, and i intend the use of the term 'interesting' in the most positive light -- it is a fun challenge to optimize a discrete op-amp.
If designing an op-amp from scratch, and VERY GOOD op amps can be designed using discrete components, with maybe a few matched pairs, it really benefits from understanding the lower level behavior of the components. The 'beta' model of transistor gain need not apply, but true design requires design down to the diode equation, understanding the capacitance nonlinearities, and understanding the deviations from the ideal. This is one reason why nowadays, it is more difficult to challenge the better high quality, general purpose op-amp chips -- the designers MUST know the physics of the device, but many casual analog EE designs don't require that much detail. (A really good EE design can and does utilize all of the details that the chip designer uses, but it is pretty easy to do a good job without knowing the details -- it is just more hit and miss.) Perhaps very importantly, the limitations of on-chip PNP transistors is less than when the 741/301 or even the TL071 type chips were designed. Also, discretes do give a wider flexibility of the parameters for the constituent transistors -- but with more matching problems. Chip designs even need to consider thermal feedback creating distortion at lower audio frequencies!!!
John