The take up the slack is due to a spring between the lever and the trans end cover. One that is taken up, your trying to push open the clutch plates. Yes a lever of some sort would be needed to go farther.
The lever looks a bit too far forward with the slack taken up with your finger. Not much, maybe 1/8-1/4" at the tip of the lever where the cable attaches. As long as the lever does not hit the trans case when you pull the clutch hand lever, you should be fine.
Now...If you were having an issue where when you let out the hand clutch lever and it goes almost all the way out before you start moving. The normal likely culprit is that you need a bit more slack in the cable. For now, just use the adjusters on the cable and leave the trans clutch lever adjuster alone, again unless the trans lever is hitting the trans case.
I set the adjusters so that when you move the hand lever it will move a small bit before you feel it trying to open the clutch plates. The more slack in the cable, the closer to the hand grip the bike will start moving, but could cause harder shifting.
Hope this helps,
Tom