Why do you think that situation is illegal? The HFT does not know you're buying shares on all the exchanges, they've only seen the shares at price P be bought o

Why do you think that situation is illegal? The HFT does not know you're buying shares on all the exchanges, they've only seen the shares at price P be bought on a single exchange (and that happens all the time without people subsequently buying shares at price P on all the other exchanges). Moreover, even in the scenario you described, that the shares were bought on the first exchange is public information -- anyone is free to use that information as they see fit (such as turning around and buying shares on another exchange, or pulling your offers at P from that exchange).