I'd really rather not read a Harry who acts like canon Lockhart. I think in the long run not being a total git will earn more friends and allies. Canon Harry is fairly humble, and turns into an excellent leader.
I don't know, whatever you think about modern celebrity culture as a concept, I don't think literally all of them are 'total gits' that are indistinguishable from a man who brainwashed children to build up his own reputation.
I'm met plenty of self confident people, some of whom are even guilty of the ultimate sin of speaking with pride about things they done or traits about themselves, and some of these same people just happen to be lovely to spend time with.
Their are ways being too confident in yourself just like their ways that having too low self esteem can be bad for you and those around you, but outside those extremes I think you can be a good person regardless and not in spite of whether your humble or boisterous, yknow?
All the arguments you have given look convincing, indeed, the choice of a hat can be accurate and complete, but there is one drawback here: people are not static characters. Remember the same Peter Pettigrew when he was enrolled in Gryffindor, but by the end of his studies he had more of a Slytherin mentality. Thus, suppose we have an average person, he has a weak connection with the principles of Hufflepuff, but the connection with the rest of the houses is even less, he naturally falls into Hufflepuff, but growing up, he acquires a personal characteristic of another house, while discarding the remnants of Hufflepuff traits. As a result, we formally get a Huffpuffian student who bears the traits of another faculty, and according to the logic presented by you, the Huffpuff Lord will not have any influence on such a student, because he is not a real Huffpuffian, but the description of the skill does not say anything about the criteria of character, there is only a criterion of belonging to the faculty.
I think it's important to remember two things. One, your example of Peter Pettigrew is one i'm glad you brought up, because I think it helps my point. Peter was a pretty rare phenomenon known as a Hat Stall where the sorting hat doesn't almost immediately decide where to place the child, and he took a unprecedented five minutes of deliberation by the hat on whether to place him in Gryffindor or Slytherin. So it's not that he slowly morphed over time to take on those slytherin like qualities, it's that they were always there according to the Sorting Hat. Now, Peter is a fascinating character in some respectes and I could go on for a while about how say, I think the fact that he was able to put up with being a pet rat for such a extended amount of time is way more of a show of Gryffindor determination or nerve then any sort of Slytherin trait like Pride, given how not only humiliating but realistically how horrible a life that must have been for any human being to endure.
However, I'll keep things brief and go with the end of his life. but as people
You-Know-Who had grafted a silver hand on to him that would strangle him if he ever showed any sign of disobeying
Him. During the breakout from Malfoy Manor, when he stumbled on Harry and Ron he was about to kill the former before Harry reminded Peter of his life debt to him. Despite full well knowing the slightest hesitation would have caused his own death, the moment he was reminded of Harry's earlier kindness towards him he was unable to go through with it, to predictable results.
When confronted with this knowledge outside the novels proper, JK Rowling wrote about how the Sorting Hat took that act as a show of bravery at the most dire cost possible that would have overwise doomed the wizarding world due to Harry's death, and that this evidence confirmed his choice of making Peter a Gryffindor. In interviews and other ooc statements, JK would refer to this as a moment of redemption for at great cost for what Peter had done at life and also talked about how he's a example that the moral universe of harry potter is slightly more complicated then 'Gryffindor good, Slytherin bad' though ymmv how well you think it made tha point, not supposed to show that the sorting hat was full of shit.
The second thing is that I actually thinking that pointing out that people's characters change improves my point rather then debunks it. Consider that the sorting hat is a magical artifact created by the four greatest wizards of their age, in a world where diviniation expressly exists, what actual magical powers it uses to judge people are poorly understood in universe, and is present in a plot that heavily relies upon vague but seemingly unbreakable prophecies. Consider also that despite being picked at the ages of 10, every year of a house seems to by and large reflect the characteristics of a house in aggregate despite you expecting to see the sort of drift from those values in quite a few of them over the years even in enviorments that go too far more extremes to instill their guiding values. Consider that this seems to hold true even past graduation, with the norm of adult characters even outside of the faculty being defined by what house they were placed in during the time in school. Also, keep in mind even the most Gryffindor of Gryffiindor who was seen as worthy of Godricks Sword, experienced a fair deal of character growth over the books that shaped him into more of that archetype.
From a doylist persective I might call this lazy world building, but from a Watsonian perspective? That tells me that the sorting hat is basing it's criteria not just on what sort of person they are at 10, but what sort of person they'll grow to be.
That makes sense?