Your next screen replacement wouldn't really be "cheaper"
With AppleCare+: $99+$79+$79 = $257
Without AppleCare+: $109+$109 = $218
If you encountered water damage, THEN it's worth it. But how many people actually encounter water damage? I personally haven't bumped into anyone with water damage in years.
Yeah, so thats $39 more for 2 incidents of screen only replacements, but if you consider that manufacturer defects will also be covered for an additional year and if you encounter water damage or the drop screws up the camera, buttons, or affects any other parts, that will make a BIG difference.
I think the AppleCare+ way is the most hassle-free way. If you're counting your pennies, maybe it would be tough choice but I think maybe all the more reason to buy the AppleCare+ because you are likely to be least able to afford a replacement unit if something happens that might require more than just a screen repair.
For people saying this is outright fraud, I am not sure that is the case.
First of all, one does not have an obligation to disclose to Apple the condition of your unit (and if you do disclose it or are asked to, then as long as you don't lie you are okay. Chances are they won't ask you if your screen is cracked, they may instead ask a general question like if the unit is working to which answering "yes" is not a lie since the unit works despite the cosmetic issue).
If they decide that it must be inspected, then obviously you may or may not pass inspection and may be unable to add it (or for all we know they'll ask you to pay for the screen replacement before letting you add it, who knows).
Also Apple may even opt to willingly let you buy the plan knowing you are going to immediately use it. It's not like they take a hit on this, you would be spending $179 right there, and you can be sure they have a profit margin on even the $79 replacement much less the $99 overall plan. It's still a profitable transaction for them, so I wouldn't be surprised if they would totally ok this plan.
(Also for fraud to exist, you have to hurt the other party, and in this case considering that the transaction you're entering into is still profitable for the other party, I am not sure how Apple is hurt by this.)
Or perhaps if you pay for the $109 screen replacement they'll let you add AppleCare+ after for next time which I think is a wise investment.
To the OP: For all the people giving you the advice not to even attempt to get AppleCare+ at this point, I guarantee you that most if not all of them would be trying the same thing if they were in your situation.