I'm not sure it's true we interact with a pure projection or idealization. If your T is totally blank state, then yes. But nowadays there's loads of Ts that are not just a blank state. I do not believe that I know my T in depth. But I know some stuff about him, and I can sometimes tell that something is not me projecting stuff on him, it's actually his personality. And he has confirmed that.

The fact that we project stuff onto them does not mean we do not need a T. In my opinion, therapy is there to help you deal with life. For 99% of the people, other people play a huge role in life. Relationships are everywhere: your job, your partner, friends. Hell even people in the streets. Things that occur in therapy are not things that do not occur outside of it. Your project things onto every single person you meet. The difference is that in therapy you can tell to a large part that these projections are actually projections.
Assume the T is totally blank state, then you both know to 100% that everything you feel and think comes from yourself. It is not a reaction to the other person. So you can analyze in what way you project stuff onto people. You probably don't it exactly like that with everyone, but there's a good portion of the people in your life where you will do it similarly. And if you know that, you can change it if you want to. Or at least you know about it.

I feel like analyzing your interaction with other people would be hard without having other people around.