I'm supposed to have gone.

I think saying “ I was supposed to go” sounds more natural when you’re talking about somewhere you were supposed to go but didn’t.

No, it should be either "I **was** supposed to have gone." or "I'm supposed to go." depending on what meaning you want to convey. Edit: There is *one* valid usage for "I'm supposed to have gone." If you are an actor in a play and your character was supposed to have gone somewhere according to the script, but you're talking about your role in the play in the *present*, then you can use this construction. Example: >"I, Robert, am playing Tim. Here we are doing a scene where Tim runs into Sally at the store. According to the script, I'm supposed to have gone to the airport, but the director has changed the plot and now I'm at the store." Needless to say, this is unbelievably obscure and you will never need to use this in normal conversation, but it's an example of how even weird nonstandard structures can have a meaning and a place.

"I'm supposed to have gone" is in the present perfect subjunctive. This tense is used to express an obligation or expectation that should have been fulfilled in the past. "I was supposed to go" is in the past simple subjunctive. This tense is used to express an obligation or expectation that should have been fulfilled in the past, but without emphasizing that the action was completed or not. Different tenses with different meanings.