Thats the point of exile, not your problem. If they don't leave, drop em in the ocean with a raft and say good luck.

You do understand the obligation of the justice system is to impart justice in a fair and humane way, correct? Considering the fact that exiling somebody by "dropping em in the ocean with a raft and saying good luck" is tantamount to handing them a cruel, inhuman death by starvation or drowning, this is not something that would be done by any rational, modern justice system.

Locking somebody up for life just makes them a bigger problem.

How?

Not only does long term incarceration not help society and turn that person into a harder criminal with nothing to lose it actually costs it money.

Simply put, this is not true. The entire point of pretty much any 1st world justice system is rehabilitation and the protection of society at large. The idea that long term imprisonment would only make somebody "a harder criminal" is baseless. You could argue for institutionalization, but that is another matter entirely. On the idea that it costs money, sure, any humane and practical option will.