Trust me, the people in prison are not all innocent victims who have been wronged by the system
They might not be 'innocent' but they are victims and they are being wronged.
and would be glad to better themselves
Compassion doesn't require that they be willing to better themselves or that they reciprocate the same respect we give them, it only requires that they can suffer.
Punishment is based on the idea that a) we have legitimate authority in 'disciplining' our equals and b) it is more important to give people what they 'deserve' than it is to relieve their suffering.
as a method of correction
You cannot correct (do you mean rehabilitate?) someone against their will. Prison does not moralize people, it demoralizes them. It makes little sense to inhibit aggression and anti-social feelings in others by behaving anti-socially and aggressively towards them yourself.
and to protect ordinary people from them.
Prisoners are 'ordinary' people and their interests should be given equal consideration as are everyone else's.
No, it isn't ideal, but few things are and I've yet to see someone propose a decent alternative.
Irrespective of whether or not prison deters crime (it does not, if at all, deter crime to the extent that most people think it does), it is still morally inappropriate because it disregards the feelings and interests of the prisoner. Individuals should not be degraded and mistreated to the extent that prisoners are even if doing so has desirable, utilitarian consequences.
If you're going to express support for an idea like this I think it would be nice if you could at least state your reasons.
"Current scientific opinion on an international basis is that punishment through imprisonment does not reduce crime rates and, in some instances, even worsens crime rates."http://www.cis.org.au/policy/winter03/polwin03-9.pdf
I admit, I haven't read the article but I think the prison system violates the non-aggression principle. It is not self-defense, it's preemptive slavery.
Im not so sure we can drop prisons straight away, society would need to drastically change first
Maybe we can start with a moratorium on any further building of prisons and the release of all non-violent offenders (I would hope, at least, that everyone can agree that drug users/dealers, prostitutes, tax mitigators etc. should not be in prison). We can also work on mending the socio-economic factors involved in a person's likeliness to commit crime.
I think the prison system needs to be changed, but I don't think it is feasible to abolish it completely, unless people stop doing the things that get them put away. Something needs to be done with people who commit crimes, and prison is certainly better than execution and more cost-effective than something like house arrest, which wouldn't even be possible in a lot of situations.
One good, temporary alternative would be to put prisoners in general psychiatric hospitals not targeted towards 'criminals' alone.