It's not that simple. (Problems are never that simple.) I live in Ballard which has a lot of people living out of RVs and tents. Many of those people don't cause problems for anyone, however, I have personally experienced:
* People shitting in our alley.
* People pissing on our garage.
* Someone shitting in a medical commode on the side of the road in broad daylight. (I admit a certain admiration for this person's self-confidence.)
* In the middle of the night, someone standing at our fence gazing into our kitchen for several minutes while gesticulating wildly.
* Furniture stolen from our front porch.
* Someone rifling through our trash. (Presumably for identity theft. In Seattle, food goes into separate compost bins.)
* Finding used needles on the lawn. (I have small children, so I had to teach them that the shiny bright orange plastic things are not toys.)
* Frequent fights and people screaming at each other at all hours of the night.
* Multiple car break-ins from car prowlers. My wife caught and yelled at one car prowler before they were able to get into one.
* When they people relocate, they typically leave a pile of trash and human waste behind. Often, RVs will dump their blackwater tank directly on the street or sidewalk. This is, obviously, a health issue.
This is just what has happened directly to my wife and I. Other nearby events:
* My neighbor owns an RV in his backyard. Someone broke into it and stole several things, including an urn containing his father's ashes. He chased after the guy, who responded by pulling a knife on him. 
* A couple of blocks away, someone was stabbed in the chest when they confronted someone slashing tires (in what I heard was some sort of turf disagreement).
* Another neighbor found a discarded gun in their bushes. They have small children too.
* Our neighbors are constantly finding trash that's been dumped in their bushes.
* Many neighbors have been screamed at, harassed, or assaulted by people that are either mentally ill, in the throes of meth psychosis, or both.
* Public parks that used to be places to play with the kids but now are effectively off-limits. 
All of this is just in a couple block radius, just in the past few years. And this is in a nice part of town. Residents in the city have had a lot of compassion and a lot of patience for many years, but the city has failed to actually come up with any effective solutions. In the past year or two, people have simply run out of. It's hard to get people to empathize with someone who is actively causing them harm.
Fundamentally, humans cannot safely live at urban density without access to the full range of residential services. You can't just "car camp". Humans produce waste. Without clean water, garbage pick up, and sewage services, each of those humans is a walking disease vector .
Safe injection sites are not a solution. If you don't address the crimes that addicts commit to afford drugs, then your injection site just becomes a crime magnet. Mental health and addiction treatment centers are good. Shelters are somewhat good but many homeless people choose not to use them because most shelters prohibit drug use.
It's not about jailing homeless people or drug addicts. It's about jailing people who repeatedly commit property or violent crime. The root cause is usually drugs, and should be treated as part of a solution. But, at the same time, other people in the city (including many other homeless people who are one of the most common victims of crime) need to be protected and feel safe. Being a drug addict should not be a blank check to steal from, vandalize, and assault people.
1. Safe injection sites, free drugs, and housing? This will solve most of your property crime + health issues, at high cost, and some moral hazard.
2. Safe injection sites and locking people up forever for property crime? If you ever let them out, without addressing the reasons for why they are breaking into cars, they'll be right back at it. This is also incredibly expensive.
3. No safe injection sites and some combination of the above? You get the same costs + problems, but also more overdoses.
4. Some other option?
1. The War on Drugs still exists, creating an expensive black market for addicts where they have to commit crimes to feed their addiction - money that goes to gangs/cartels. Researching treatments is difficult due to drug scheduling. Treatment options are limited (like "free drugs").
2. When a particular locality attempts to address these issues in a callous way (like busing), it "solves" the problem for locals, but of course the people still exist and just move to the next town that is not cutthroat. This leaves a disproportionate amount of the problem to those living in cities, where the most services/shelter options are available.
To truly solve the problem, we need to end the War on Drugs, build housing, and properly fund treatment centers on a national level.
Your first option is about as good as it can get when trying to solve this problem using local tools. Safe injection sites, methadone/similar, and housing are all far cheaper than just a subset of what the chronically/drug-addicted homeless cost already and they actually attempt to address the issues of addiction and homelessness. Without housing, drugs/treatment, and injection sites you get: people on the street buying from the black market spreading disease that have numerous emergency room visits and nights in jail, costing everyone far more money than the housing/treatment. But folks in cities will still be paying far more than their fair share to do so and they'll be treating a lot of outsiders from places that don't offer those services, but should - the causes of the problems will still exist elsewhere.
If you commit property or violent crime you go to jail. Rehabilitation services should be made available there.