I don't offer clinical autism evals (I do autism evals on the forensic side) but it does come up quite a bit in my patient population. Interestingly, one of my recent consults was so obviously autistic I knew it before I met him and confirmed it within minutes and he was adamant that he was NOT autistic.
I think it is good to have a healthy skepticism and bear in mind that the majority of autistic individuals can't work full time or live independently nor do they marry or have a longterm romantic relationship. At the same time, there is a wide range of outcomes and a significant minority of autistic people won't meet criteria for an ASD diagnosis as adults.
Differential for these consults includes patients with borderline, narcissistic, avoidant, schizoid, obsessive-compulsive personalities, PTSD and complex developmental trauma, social anxiety disorder, schizotypal disorder, highly sensitive persons.
Other things to note is that a lot of people do have autistic like traits but won't meet criteria for ASD (either because of lack of any language impairment or because their traits don't cause significant impairment in social and occupational functioning).
Patients can definitely be correctly diagnosed for the first time as adults. This can the case if they had other problems as children that meant the autism was overlooked, their parents were neglectful, they were from a different culture/country with less access to this kind of care, they were able to compensate to some degree, and many women present somewhat differently. I had one patient who had significant intellectual disability and an interesting neurogenetic diagnosis with autism. No genetic testing was ever done and the autism was completely missed. This patient was unable to live alone, work, and had textbook worthy brain imaging and was in their 5th decade of life before the ASD dx or genetic testing offered by me.
We also see patients with ASD presenting to memory clinics for evaluation of bvFTD even though their behaviors are not new and they've always been socially inappropriate and weird.
In my forensic work, I also see people who weren't diagnosed with ASD as children. There is a lot of BS with autism as moral exculpation for bad behavior, and most of them time they don't have autism, but we definitely genuine autism first diagnosed at the time. Of course, the courts rightly look more suspiciously at de novo diagnoses.
My main pet peeve is that the ADOS is NOT the "gold standard" for autism evaluation and should not be used as a standalone tool to diagnose autism. The "gold standard" is a clinical evaluation with access to collateral sources for developmental history by an expert in autism who might be a developmental pediatrician, psychologist, psychiatrist or neurologist. The ADOS was never intended to be used as a clinical diagnostic tool and while it is certainly useful, it is neither necessary nor sufficient for an ASD diagnosis.
As an aside, doing autism evaluations can be potentially very lucrative in the right setting. Bonus points if you speak Mandarin.