I think what you're suggesting is a having a call auction every minute. There may be exchanges that do this already, but there'd still be advantages to being high frequency (i.e. waiting until the last possible nanosecond to submit your order and take advantage of whatever you can find in the order book before the matching engine does its thing...or submitting early if you have other information, there is little liquidity on one side or the other and the time/size order priority is in play).
I think the HFTs are pretty easy scapegoats these days, but on closer examination, any criticism of them is a criticism of capital markets in general. People/robots/algorithms with more information are always going to outperform the retail investor. If you really want to curb HFTs a transaction tax is the only semi-effective thing I can think of.