[joshuamorton]

It's worth reading the abstract of the paper you indirectly cite:

> The lack of negative impact on voter turnout cannot be attributed to voters’ reaction against the laws, measured by campaign contributions and self-reported political engagement. However, the likelihood that non-white voters were contacted by a campaign increases by 4.7 percentage points, suggesting that parties’ mobilization might have offset modest effects of the laws on the participation of ethnic minorities.

Or in other words, the authors conclude that voting laws don't ultimately affect turnout, but that's confounded by a nearly 5% increase in GOTV efforts. While it's probably wrong to conclude that a 5% decrease in GOTV would reduce turnout by 5%, there's almost certainly some offsetting impact there.