Re: Differential pair
That is a good point.
Supply sensitivity which is the application of common mode rejection in most OTA's is also defined by the output stage. So if the input stage losses e.g. 6dB voltage range in comparison to a pseudo-diff-stage the overall, to be clear, relative rejection could be worse. The focus on input rejection is historic because most opamps have high gain so input stage CMRR matters. But OTA is a different story.
To give you a small hint; there three CMRR effects!
1. Simple ratio of Diff-to-Diff versus CMD-to-CMD gain
2. Mismatch based CMRR
3. Dynamic CMRR, if the signal swing is big CMD-signal could couple in or mixed