If all cars cost a $1000 co-pay no matter what car you bought, who's gonna buy the Honda Accord? However, throw price into the mix and Honda Accord becomes a very popular choice.
There's no huge, magical saving of money by running all medical spending through insurance providers. In the end the doctors are going to get paid. It is a matter of whether you pay them directly or pre-pay an insurance provider and they pay the doctor. Insurance is about mitigating the risk of rare but financially ruinous events (eg, cancer or serious trauma). There isn't any risk to mitigate with a flu shot or a bad cold or a mammogram. You insure your car against accidents, not oil changes and flat tires.
As for the poor problem, that can be solved separately by providing the poor a stipend for health care. No need to re-architect the whole system because it doesn't work for 100% of the population.