Can iPhone battery apps actually prolong battery life?
Solution 1:
From what I understand, iPhone apps don't have the power to regulate the power consumption of other apps and iOS system processes. These apps sound like snake oil to me.
Solution 2:
Apple themselves recommend a deep cycle every month:
Be sure to go through at least one charge cycle per month (charging the battery to 100% and then completely running it down).
If the app reminds you to do this every 30 days, then yes, it will improve your battery life. Unfortunately, I've seen some apps that tell you to go down to 20% and then open the app while it is charging. That isn't letting it "completely run down", and so, it would do nothing for your phone.
Besides reminding you of doing a deep cycle every 30 days, I don't see how any app could improve your battery life. If anything, it would ruin your battery life by staying running in the background.