If you legalize drugs you will create more addicts, more people will try them and more will become addicted as a result. And you will get more over doses as a result of that.
If you regulate the quality of the drugs, you will end up making them weaker/watered down and addicts will go back to their old dealer to get the stuff that gives them the high they need. And there is no addict that will stop using after their prescription is up, they will go find more and they don't care about the consequences.
If you are regulating them and taxing the heck out of them you are going to make drugs a lot more expensive than they are on the street, the people who were already addicts will realize this and will either only try the legal drugs once before going back to their dealer, or not try them at all. And the people who become addicts after trying drugs because they are legal will quickly realize there are cheaper drugs out there that give a better high.
Do a lot of addicts feel shame about what they are doing, and hide it as well as they can? Yes, they do. Will drugs suddenly becoming legal make them take the step to seek treatment? No, it won't. To genuinely want to seek treatment usually requires an addict to hit rock bottom, or to have a major event happen in their life(a bad event the huge majority of the time). Making drugs legal is not going to make them hit rock bottom, if anything it will give them another excuse to keep using, "hey family/friends it's legal, so shut up and leave me alone" would be a very common thing for an addict to say.
I agree with you that we need to change up our approach, sending more addicts to rehab/counseling instead of jail would be a good thing. Legalization is not the answer.