Because high voter turnout results in more Democrats being elected. Lower turnout elects more Republicans. Simple as that. Therefore, anything that can make it more difficult or time consuming to vote is a worthy effort on the part of Republicans.
1. Discourage or ban voter registrations
2. Restrict or eliminate early voting.
3. Close polling locations, particularly in areas which tend to vote democratic.
4. Restrict mail-in ballots.
5. Outlaw providing volunteer mass transportation to polling locations.
6. Purge voter rolls as close to election day as possible.
7. Require government issued ID to vote.
8. Justify all of these actions on the basis of maintaining election integrity. Never mind that none of these have ever been a problem in the past.
Democracy was all good and fine, as long as old white straight men were in the driver's seat. Now that the complexion of the American electorate is changing (women, gays, minorities, etc.) those old white guys see themselves being pushed aside and they are not about to give up without a fight.
At this point, the GOP is not even worried about backlash when their true motives are exposed. Either they (old white straight guys) figure out how to maintain control or they would just as soon burn the whole thing down.
The really sad thing about all of this is how
the GOP is able to convince many of these measures' targets that it is in America's best interests that they should support voter restrictions.