The urban myth I heard was PE not relativity, because practicality.
There is a simpler and better explanation: Einstein's
contribution to /special/ relativity was slight compared
to
Galileo
Lorentz
Poincaré
Minkowski
and the 1921 prize committee was well aware of this.
As for /curved/ spacetime and /general/ relativity, that
was Einstein's doing ... but in 1921 it was hard to know
for sure where that was going, hard to know whether it
would stand the test of time.
Actually the committee was devious: Einstein's citation
reads
"for his services to Theoretical Physics,
and especially for his discovery of the law
of the photoelectric effect"
The "services" part could mean almost anything.
This part makes sense, since Einstein did a lot of
stuff, including atomic theory (Brownian motion, the
diffusion/mobility relation, why the sky is blue),
GR, some contributions to SR, et cetera. Later he
made some contributions to QM (EPR, Bose-Einstein
statistics).
I reckon GR was worth a prize by itself. The other
things /individually/ might not be overwhelming, but
collectively they are impressive.
As for the second part of the citation, IMHO the
committee screwed up by mentioning the photoelectric
effect in particular. I reckon Einstein was just
wrong about this, and it set the development of QM
back by many many years. Planck warned on Day One
that the evidence did /not require/ energy to be
quantized. Einstein ignored Planck's warning and
over-interpreted the photoelectric observations.
It wasn't until 1963 that Roy Glauber cleaned up
the mess, giving us a systematic way to understand
and deal with non-quantized states. For pictures
and discussion of how this works, see https://www.av8n.com/physics/coherent-states.htm
It wasn't until 2005 (!!!!) that the committee got
around to giving Glauber the prize for this.
Maybe in another 100 years or so the physics textbooks
will catch up with what Planck said in 1901 and what
Glauber said in 1963 ... maybe they will stop talking
about "quantum leaps" and stop claiming that energy
is necessarily quantized.