I would like to speak about treatment for various illnesses, physical and psychological.
Would the expression 'health treatment' be commonly understood?
So far, it is not a widely used expression. However, 'mental health treatment' is.
What's your stance as a native English speaker?
Treatment can apply to a lot of things. You can have beauty treatments, hair treatments, treatments in the sense of a summary of how a screenwriter proposed to adapt a novel, and just generally talk about treatment that you received from a business. So, some sort of qualification is sometimes appropriate.
I say sometimes, because if you're at a dentist, or a beauty salon, or whatever, what type of treatment is involved is obvious. As always, context is very important.
Without that context, however, most treatments related to health are called medical treatments, or sometimes more specifically surgical treatments, pharmaceutical treatments, dental treatments, mental health treatments, and so on. In some places, the word medical is restricted to things done or overseen by medical doctors, so dental treatments would be excluded from medical treatments. Mental health treatments are, in my experience, generally included in medical treatments.
However, if you call it a medical treatment, there will be an expectation that it is based on solid evidence, and terminology like that might be legally regulated (it is in a lot of countries) so you need to really demonstrate effectiveness and register with a regulator before you can market it.
Health treatments would be understood, but it's an awkward phrase and people would wonder why you didn't say medical. It's far from unheard of, as a term, but nowhere near as common as medical treatments. Healthcare treatments is a much more recently-emerging phrase, and it doesn't have the same jarring effect, but it's still not widely attested and may be regulated like medical treatments. There's also a much more rarely-used term around, health-related treatment; it's not widely attested, but it would be understood and not seem unnatural, to me.
The trick here is to think of what you want to say, and decide how few words you can say it in without being misleading or ending up unnatural. It can be better to use several extra words and be idiomatic than the be more succinct but unnatural.
Nothing wrong with the previous answers, I just think OP was asking for something a bit more simple and direct in answer.
You ask if 'health treatment' would be commonly understood, and the answer is absolutely 'yes'. But, as SamBC says, there are lots of other phrases that would be used more naturally by native speakers first.
You ask, by implication, why it is not a particularly common phrase. It is because 'treatment' inherently implies 'for health' in most contexts, and because other phrases like 'medical treatment' exist for dealing with specific situations.
'Mental health treatment' by contrast uses a fixed noun phrase 'mental health' and links it to 'treatment' to make it clear the treatment is specific to mental health.
So it is:
[Mental health] treatment.
Not
Mental [health treatment].
Treatment can mean medical care, which is
the provision of what is necessary for a person's health and well-being by a doctor, nurse, or other healthcare professional
, so health may be omitted.
Any of treatment / medical care / health care is widely used and should be commomly understood.
