No insurance will cover past medical bills. Your sickness is not going to wait until you get insurance to get worse. So by the time you find out your illness, you've already racked up medical bills, that your new insurance won't pay for since they were from prior visits.
And in the mean time, if you have avoided insurance, you will be paying fines (taxes) for not having insurance. That's why health insurance is MANDATORY, because I don't want to pay for your stupidity and ignorance.