Creating long tailed pair differential amplifier using NPN vs PNP

The long tailed pair is the basis for differnetial amplifier and its first stage. I have usually seen it constructed using pair of NPN transistors in common emitter configuration with their emitters feeding into a single emitter resistor. The common mode rejection ratio of this can be improved by connecting a current sink made using NPN at the emitter instead of emitter resistor. The gain of this can be significantly increased by connecting a PNP current mirror current source shall force same current into collector of both the transistors in the pair. This shall replaced the "load" in the common emitter configuration of the transistor pair i.e the collector resistors must be replaced with the PNP current source.

Why is this same circuit not build by inversion i.e the pair contains PNP transistors instead of NPN, the current sink at emitter becomes current source using PNP instead of NPN and the current mirror shall sink current using NPN rather than source it? It should work that way too right?

When you have a PNP as the input for your signal, it requires that you reference your signal to the positive supply. Bias current flows out of the base terminal. It will work, although it forces us to think in different terms from the NPN behavior which we tend to be accustomed to.

NPNs always have better frequency response than PNPs
of similar construction (base width, breakdown voltage)
and for an input stage that could go either way, they
always get picked. And lateral PNPs, forget about (slow
and lousy hFE).

However some applications (like single positive supply,
input range includes ground) will like the PNP better
because it doesn't choke off the tail current with both
inputs at 0V.

Study the datasheet and transistor level circuits of popular OPs and find out that PNP input stages are frequently used to achieve e.g. a specific common mode range.

These ICs design either live with the poorer performance of PNP transistors in the standard planar process or use special high performance processes that provide dielectric isolated PNP.