Personally, I think an open anointing is a good idea: there’s so many people with so many medical issues who can benefit from the grace of this Sacrament, and sometimes it’s the best consolation you can get, especially if you have moderate mental health issues as I do. Years ago, when I was two and about to undergo eye surgery, my mom wanted to have me Anointed, but I was considered much too young for it. I still have a lot of medical issues – bad allergies, depression with occasional bouts of suicidal thoughts, and Asperger’s Syndrome (a form of autism) – so recently at Mass, when the priest invited the sick to receive the Anointing afterward, I almost got up to receive it, but I hesitated. My mom looked at me and gave me a gentle nudge toward the altar, so I got up to receive it…
And I’m glad I listened to that nudge; I swear sometimes Our Lady speaks to me through my mom: after the Anointing, I felt as though a weight had been lifted off my shoulders and the churning sensation in my head which sometimes comes when I’m overstimulated just went away leaving behind the profoundest feeling of peace which lasted for several days. I’m tearing up just posting about it.
I agree, it’s a sacrament that can be easily abused (so can any of the others): getting the Anointing for a stubbed toe or a nicked finger would be absurd, but I wouldn’t pry into why a person went up to receive the Anointing.