It would not change anything significant about HFT besides removing the H. There would still be a technology race to execute trades as close to exactly 1 sec as possible.

HFT firms make money by being the first to grab trades for tiny price deltas. If the law said trades could only execute on one-second intervals, the deadline to be first to grab a trade would become a tempo defined by human law, instead of a steady lag due to physical law. But there would still be a deadline, so companies would still race.

That would push spreads apart a bit (increasing the costs of trading for everyone) but it's still clear that someone would be need to making markets. And it would still be cheaper to have computers do this instead of humans.

Most of the firms I worked for rested orders for days or weeks. Having to rest orders for a second would not materially change their trade other than make them slightly less likely to get into the top of the book, thus increasing the spread.