Different designers favor different approaches,
I got into things young and have always been
more of a visual / "gut" sort while it's not very
surprising that freshers or students favor the
math heavy approaches they've been taught.
"Gut" comes later, or somewhat, or not at all.
But math needs numbers and those, you (OP)
lack. You need gm (at sane operating points)
of the gain element and you need the Zout of
all parallel devices attached to the gain node,
and whatever gain can be had from the diff
stage / current mirror (often, not much besides
the differential-to-single-ended conversion).
When I started in this game there were many
old timers who would bag on simulation and
insist on derivations. At my first employer there
was this guy who taught a in house course
where he derived the h-parameter expression
of a 200-transistor op amp (he was famous for
his designs' elaborateness) starting from the
Bohr model of the hydrogen atom. Week after
week it went on.
You can go too far with the "mathing".