I like *neomerlin's quip about first person not inserting the author any more than third person inserts some guy called Jimmy. And I agree with the people who have mentioned that any character will include some element of the author.
That said, I really don't think first person stories are intended to have the reader include themselves as that first person narrator. It doesn't match up with how first person is used day-to-day, for one thing: when I say "I went to the shops this afternoon," I'm not inviting you to imagine that you went instead. Also, second person really is used in that way: just look at all the SomeGuyxReader junk that turns up on the front page. Or those "choose your own adventure" books where "YOU are the hero!" When I read first person books, I'm always very aware than someone is there, telling me this story.
Personally, i'd say first-person is better for character-driven stories; by which I mean, stories which rely a huge part on what's going on inside the character. When I read a first-person story, it shouldn't, ideally, resemble a narration, but it should instead resemble the character's train of thought as they experience the events of the story, and reveal facts about themselves that no-one else in the story knows, but only when it's relevant to do so, otherwise it just seems like unnatural exposition. So, in a way, it would add a whole new layer to the story that would be completely missed if it was told by another character. Granted, the same thing could be accomplished if you used some kind of invisible, all-knowing narrator, but personally I find that... odd, to say the least.
When it comes to self-insertion as you define it, i'd say, and I think you're saying (correct me if i'm wrong), that that can only really be possible if you fail to reveal anything significant about the character that would set them apart from you as a person, or otherwise establish them as their own character with their own thoughts, beliefs, and personality; so if any old Joe on the street can assume the role of the character, then that kind of defeats the point of having a first-person perspective in the first place, in my opinion.
Personally, I prefer first person to third. Not that I don't like third person, but many of my favourite books seem to be in first and neither would I consider them to be self-inserts. Especially since they often feature multiple first person narrators.
When it comes to my own writing, I write both for the sake of variety and practice. But I don't really like the idea of an omniscient narrator following the characters and describing their actions or just being able to read one character's mind to describe it to the reader.
I'd agree that it's probably easier to write a self-insert piece in first person and easy for an inexperienced writer to screw it up and start writing in their own voice instead of the character's. But in the hands of a good writer, I find first person is an excellent way to see things through a character's perspective and understand their mindset better. Just my opinion, though
In most first person books I've read, the perspective is very much not of a self-insert, hence why I'd disagree that first person is naturally aimed towards self-insertation. The only examples I can really think of that aren't teen literature or obviously geared towards people's fantasies would be books like To Kill a Mockingbird and Oranges Are Not the Only Fruit, where they are partially autobiographical.
It might seem like first person is used for self inserts, though, because it's easier to screw up than third person, in my experience, and inexperienced writers are way more likely to lean towards self-inserts. But I've read a few crime thrillers (I don't really like the genre so I haven't read many) which are written in third person but also carry at least some degree of wish fulfillment for the writer.
Writing in first person doesn't necessarily mean self-insert, but I agree with the "roleplaying" to a certain degree.
When I am writing in first person, I see the situation and setting through the active character's eyes, I notice what they notice, not more. I forget to mention details the narrator/character won't think about even when a reader might want to know more. Even when the setting is different from reality, I only mention details when they are important or unusual for the narrator/character at that moment/in that particular situation.
As for physical descriptions of the main character. Hm ... I try to give some information when it makes sense and fits. Through action or dialogue if possible. Preferably when it shows us more of his personality, too.
First person and third person both have their advantages and disadvantages. You can have a badly conceiled "improved" copy of yourself in a story written in third person, too.
I wonder where the self-insert is when I write as a person who is nothing like me and who is far from being the person I would like to be. I wouldn't want to live in the world I am still building, not really, and my main character ... even though I feel far more attached to him than is reasonable I wouldn't want to meet him in real life (even though I would love to see more characters like him in books, movies, games, what ever ... yes, yes, I know that these are different media which work differently). Writing in first person sometimes feels like someone from a parallel universe and/or from the far past was channeling me. There might be some deeply hidden self-insert or wish fulfillment, but should I really search for it? I tend to over-analyze things anyway, and there is no need to resurrect my inner editor after I flushed her ashes down the drain.
The only time I do self-insertion is when I'm making fun of myself. Otherwise, I prefer to write about people who aren't like me.
I don't think one could paint all first person narratives as self-insertion. Random Acts of Senseless Violence by Jack Womack is an apocalyptic sort of tale from the first person point of view of a twelve-year-old girl. I highly doubt that Jack is Lola, though she might share one or two of his qualities.
Twilight, on the other hand, and 50 Shades of Grey are very blatant self-insertions.