[...] What exactly is the cause of the crimes and problems?
The problems in the US wrt to homelessness would be:
- Lack of affordable healthcare, meaning that any significant mental illness, depression, pain, or other condition making it hard or impossible to work means it's very easy to fall off the wagon.
- As above but then seeking drugs (opioids typically) from dodgy doctors who prescribed them because they were getting kickbacks from big pharma or bribed by desperate patients. Alcohol could also be involved, the US has very cheap alcohol in many states and limited resources to deal with alcoholism.
- Those people then being unable to afford the opioid script (due to loss of income) or alcohol or whatever other coping mechanism they have, and therefore going to harder street drugs like heroin and meth, which have painkilling effects but obviously other significant side effects. Due to these drugs being typically cut with other hazardous substances further illness or dependency can develop. Crimes may be committed to ensure income for these drugs, as withdrawal from harder opioids is no joke (can be fatal).
- The lack of a coherent drug policy, basically just "drugs are illegal and possession of drugs is illegal", making it a crime to possess drugs even just for personal use. These people then end up in the legal system.
- The lack of a coherent housing policy, so if you become unable to afford rent or mortgage, you are just homeless. Try getting a job or bank account without a fixed address - it is incredibly difficult in most countries, including the UK.
- Even if you do manage to get clean through sheer willpower (some states do fund drug rehab) you are going to find it incredibly hard to get a decent job once you've got to this situation, because employers don't want to hire ex-cons. My understanding is that most criminal records are never expunged in the US, and even if you do have it expunged from your official record, you do still have to declare this to the employer. Comparably in the UK, for all but the most serious offences, a basic criminal record check will not show history more than 6 years ago.
- Combine parenthood with this and it's very easy for children to be born to single parent families or broken households, and all the data shows kids in single parent families have worse outcomes than those with two parents.
Not every country gets these things right, the US is not alone. However, the best countries understand that people are fallible, and that given the right care and attention, most people will end up as good, contributing members of society. It is absolutely the case that there are some people that will steal and commit crimes regardless and I would agree that the UK fails to properly deal with repeat troublesome offenders (as well as the US). However, that doesn't mean you shouldn't try to fix whomever you can.
There are a lot of studies that have analysed why people become drug addicts. It's not usually moral failing or lust or anything like that, but loss of family structure, illness and income are usually triggers.