To me it sounds like old fashioned stage fright. You are expected to perform a service while someone is watching you. Everybody gets nervous. Sure it's easier on the nerves during rehearsals. No audience, you don;t have to hold for laughs or reactions from a huge group of unpredictable strangers.... But you must remember that ultimately you are there FOR the audience. The play exists so that strangers will see it, not so the actors can go through the motions just for fun.
It's the same for reading cards. It's easier on you to read by yourself with nobody around. Less irritation, less anxiety, you can go at your own pace. But ultimately it's not about your comfort or needs, it's about the person you are reading for. Consider their comments, laughter, praise as an actor considers the reaction of the audience. The sitter's interaction and presence should empower you, not annoy you. Their comments can assist you to understand them and their cards better, just as a living audience can influence and enliven an actor's performance.
I can't stand reading without the querent present. I love having that person right there. If I'm wrong or if something's not clicking, I know it immediately by their face, by every little comment, every hmm and ummm. If they exclaim all of a sudden, "Oh my God! How'd you know that?!" I match their intensity and be right there with them. If they hate the reading, their disappointment whips me back into reality and causes a new focus, a new drive to get on track and make it work. If I completely fail... Well...nobody is perfect. It makes me all the more thirsty for the next reading...I'm gonna get the next one dammit!
If you want to read for strangers in real life, right there, try to come to grips with why someone else's presence irritates/distracts you. Are you there for them? Or are you there for some other reason? Are you reading face-to-face because someone told you that you will never be a "proper" Tarot reader unless you do so? It's possible that in your heart of hearts you don't really WANT to read for strangers face-to-face, and that's okay. Some querents out there may not want face to face readings. There's no need to try to do something you dislike. Find what fits for you.
I'll take the rush of live reading...carpe diem!