Lots of parishes have done regular Healing Masses with anointing. It’s generally not people with a cold or hangnail. It’s elderly people, cancer patients, people in wheelchairs and the like. My dad was a partially paralyzed stroke victim for the last decade of his life, and my mom used to take him to these Masses. There was nothing charismatic about them as my mom couldn’t stand that stuff and wouldn’t have attended if it was that. Just a plain vanilla Mass with anointing afterwards.
In recent years I have seen some parishes want you to sign up in advance for the anointing. I presume that’s first of all so the priest knows how many people to expect and can plan accordingly, and second, so that people with colds and hangnails who also aren’t elderly don’t just show up expecting to get anointed. Also there are likely people who look visibly okay but have serious conditions that don’t show, like my friend with severe diabetes.