If coffee is supposedly so important, why doesn't it have its own support group(s)? ~

How do you know it does not?  Would guess there are many groups including clubs, businesses, supporting industries, etc. So many people go absolutely crazy over it!  Oh I gave up that habit years ago. 

JA is the president of one.

HERE you go: https://caffeine.supportgroups.com/
I looked because I was sure I would find one, but I never guessed it would be that big "31082 Members Strong and Growing"

It does. They meet in coffee shops every morning.

It does.  It's called N.A.   It is for addicts addicted to everything else drug-related besides alcohol.

Caffeine is a big one.  It can wreak havoc on the nervous system especially after getting sober.

The nerves are already compromised.

Then add some STIMULANT.   I'm convinced this helps people relapse.