Oh, I agree completely about the lawsuits - the lawsuits are a big part of the problem - both with the cost of insurance for people, and the cost malpractice insurance for practitioners, especially doctors.... which cost is then passed on to patients, in the form of rates.
I'm not as sure about the copays. The purpose of insurance premiums is to offset the cost of medical treatment if and when it is needed - therefore, the copay is intended to be the difference between what you've already paid (in premiums) and the cost of actually seeing the doctor, while still keeping some of the burden of payment on the individual patient, instead of spreading it to all members of the insurance group. Insurance can somewhat be likened to membership in a grocery warehouse such as Sam's or Costco - I pay for the membership, which helps offset the cost of the facility; then I pay for what I use, which I get at a lower price because of the volume buying made possible by combining the purchases of all of the members.
I'm not saying there aren't problems - there are some horrible problems with heath care, and cost and accessibility are high up the list - but neither is it all bad, either.