1) Residents
as academic centers expand, increasingly the new psychiatry faculty positions may have little or no contact with residents. Plus residents rotate at the VA, state hospitals, jails, private hospitals etc. There is nothing stopping you offering a resident rotation in your own practice and I know of several groups that do so. Even Kaiser has residents in some places. Plus outside of inpatient or consults, residents probably aren't much help. The increasingly onerous requirements by institutions/insurance companies etc means that in many places it's not as cushy to have residents as it once was, where attendings would do pretty much nothing.
2) Fancier business cards
the fanciest business cards I've seen are private practice forensic psychiatry ones. academic centers often provide pretty crappy business cards and you can get the faculty title without working at said institution to put on your business card if you want
3) The really weird cases
This is definitely true.
4) Ability to curbside colleagues PRN
I get curbsided by my friends out on the real world all the time. There are many listserves, FB groups, group texts, email groups, and in-person peer supervision groups for everything from psychoanalysis to brain stimulation
5) Teaching
You don't need to be in academics to teach. It's pretty common for people in non-academic settings to teach med students and residents.
6)Did I say already about the business cards?
pfft