"Romney isn't responsible for Romneycare"
Romney was a Republican governor is a deep blue state with a state legislature about as far left as you can get. Romney vetoed, what you call Romneycare five times before reluctantly signed in into law. Are you suggesting it was Romney who dreamed up and proposed, what you call Romney care? Seriously?
If by destroying it, you are talking about getting the central government out of the equation, than yes it has to be destroyed in order to make it better. 
Raising taxes or cutting taxes neither one means "healthcare". That is simply stating how deeply the central government has their noses in the health INSURANCE industry.