While carrots and APAP are both in common use by the populance, carrots do
not provide instant relief from sudden onset of pain. When you burn yourself
with hot grits, you can either stand there and think "you know, if I had eaten
carrots instead then maybe I'd be in a better mood about burning myself with
hot grits" Or you can take a pain reliever.
So we need pain relievers, not just carrots.
Carrots also do not do another thing: kill you if you eat too much, with "too
much" being something you could get down in a single swallow, or gradually
take over the course of a day without any stomach cramps to let you know
you are doing something fatal. Carrots don't kill people or cause intractable
medical expenses when used improperly, barring some rather deviant
practices (sometimes involving hot grits as well).
As such, it's very important to understand the reasons why a person might
use these substances, so that we can educate the public about which
substances to use under what conditions. If APAP can help a person avoid
using a more damaging or addictive psycoactive phrametceutical, but
has to be used with care, we need to know that.
Anyway, scientists study diet just fine. They are even finally getting around
to studying intestinal flora in better detail. Of course there is a funding
bias when big pharma levels of money are involved, but that's just capitalism
and greed doing its usual damage when we fail to set good boundaries for it.