You've already got your response in Cory's write-up. He quotes one of the people responding to Kris Kobach's commission:
“DO NOT RELEASE ANY OF MY VOTER DATA PERIOD,” wrote one voter whose name and email address was published by the White House.
“I removed my name from voter rolls. And I'm a Republican!” wrote one voter whose name was published by the White House.
A government commission's aggregation of voters' names, dates of birth, addresses, and partial Social Security numbers into one big database is going to make a fair number of people who are concerned about their privacy not want to sign up to vote. That in itself sounds like voter suppression to me.
And, as Kris Kobach said on NPR's Morning Edition, he intends for the government to use the information to determine if there's evidence of voter fraud -- which implies there would be some sort of consequences he would recommend if his commission somehow determined there was such evidence. Which, in turn, implies that he could use his commission's findings to suppress voting.