Actually, a fairly large number of people do get addicted accidentally. It often starts with a serious injury, leading to prescribed painkillers, and even using as directed by your physician can develop a dependence. Not to mention those with chronic pain who can't just stop taking them. And that dependence can take over and escalate very easily. I've seen and heard of plenty of hardworking upstanding people one would never expect becoming addicts and eventually turning to illegal means to scratch the itch.

And then there's the other end of things, where you've got young teens experimenting and getting hooked while they are young and stupid.

Or those who are being abused or suffering mental health issues with no access to mental health services, and end up self-medicating just to get by. You can say 'they should have just gotten help' but it's hardly that easy, even for an adult, and you can't expect a 14yo kid with apathetic (or worse) parents to figure out how to get help for themselves or even know that they need that sort of help. Never mind the stigma associated with seeking help.

So no, even look at morality and not cost, it's very closed-minded to assume all drug addicts should be held to blame for their own addiction and just left to wallow in their misery.