Insurance is complicated, particularly health insurance.
In the United Kingdom, for example, the overwhelming majority of people support the National Health Service, but a number of them don't realise that it doesn't technically exist any more (since the Health and Social Care Act 2012 was passed). The reason it worked was, largely, because everyone paid for it via National Insurance contributions, deducted directly from your salary. What this did was effectively remove the ability to avoid paying for health insurance when you didn't feel you needed it, and thus increasing premiums for those who felt that they did. It's no secret that young, healthy people don't feel they need health insurance - while those who are older, or have existing health problems, are more likely to have a policy.
So I suppose the OP's question is answered there: companies provide policies to people more likely to be sick, because they wouldn't have anyone to sell policies to otherwise.
Now I can't pretend to fully know the American system, but my understanding is that this was ultimately what the Affordable Care Act (Obamacare) was, in general terms, designed to replicate. Stop health tourism, ensure everyone can receive primary care when they need it, and pull down premiums for those who take out policies. Unfortunately, it didn't work especially well because America isn't Britain; Americans view the world quite differently in a lot of subtle, but important, ways.
Maybe the question is much simpler - what do you think health care should do, and how do you think it should be provided?
Thinking about that is potentially more fruitful than simply arguing that people who get sick shouldn't be insured. The logical endpoint of that is insurance companies that sell policies they never pay out on, because nobody gets sick; it just becomes another upward transfer of wealth.