I'm not really sure where I fall on this answer, so I'm going to type out my reasoning and see where it leads me... hope that's okay.
On the against-sorting side:
I would agree that there is some serious negativity generated by the sorting system, especially in the case of Slytherin house. Poor Slytherin is pretty much the designated "evil" house, which, I've always thought, makes it a bit of a self-fulfilling prophecy. I mean, if everybody else acts like jerks towards you and thinks you're a mini Death Eater, you might as well just throw in the cards and act like a jerk. To be fair, the series is told from a Gryffindor point of view, so it may be their bias (maybe Hufflepuffs and Ravenclaws are arch enemies as well?), but even so, by the end of the series, everybody is decidedly anti-Slytherin, which may be warranted for the children of Death Eaters, but that's only maybe 5-10 kids out of the whole house.
This evil designation of Slytherin also causes some serious security issues- the belief that only Slytherins become bad wizards (a belief we see as early as book 1, thanks to Hagrid) leads to ignoring potential traitors like Peter Pettigrew. One could argue that it was also easier for the Wizarding community to vilify Sirius, as he came from a traditionally Slytherin family.
There's also the issue that GOOD Slytherins don't seem to be as highly regarded by the rest of the Wizarding community as those from other houses (though there are obviously fewer of them mentioned, they do crop up here and there)
On the pro-sorting side:
1) Tradition- there is something to be said for tradition, especially when running an ancient wizarding school. I would think doing away with the sorting would cause some kerfuffle amongst the community. This is obviously a minor point, but still thought it deserved a mention.
2) Not all competition is bad- Rivalry isn't always a bad thing, at least in moderation.
3) Incentivization of good behavior- Going hand in hand with the "positive rivalry", there's the fact that the system of earning and losing house points is an effective way for schools to monitor students behavior. It would be possible to do this on an individual level, but in general it would be more effective as groups, since that makes you accountable not only for your own happiness, but also others, promoting team spirit. Whereas if you got individual points, and you just happened not to care about it, you wouldn't participate. So the school would have to resort to either mass incentives for individual points OR come up with a different way to punish kids (and Dolores showed us that isn't always fun).
4) Sports- quidditch. Might be possible to do without houses, but you would probably wind up with the good players all joining one team and crushing the others. This way, everybody has equal chance of getting a good team together.
5) Slytherins did kind of bring this on themselves- Or more specifically, Salazar did with his elitist attitude, made more of a problem when Lord Voldie happened to be a Slytherin. So while it is totally unfair to punish kids who might not be total jerks by making them believe they are total jerks, they are treated this way because... well... the most noticeable of their house are total jerks.
SO I think I do have to come down on the side of KEEP the sorting.
I will say however, I think it would be a good idea for the Sorting Hat NOT to take into account the students choice (as he did with Harry). If everybody knows Slytherin is full of evil, than what does that say about the type that would pick that house? If the SH just tossed everybody into the house they actually fit best with, that wouldn't be a problem. Also, it would mean slightly less cliqueness, as people who were friends pre-Hogwarts (especially siblings or cousins) would not be able to choose the same house... therefore, they would still talk to each other and hang out, and would introduce their friends to one another, so people from different houses could form better friendships. So I would keep sorting, but with reform.