Let's look at some facts and some projections for Rizzo. In 2013, he had 690 PA, 606 AB, .233 BA, .323 OBP, .419 slugging avg,and a BABIP of .258 (vs. .310 in 2012). If Rizzo tried to bunt for a hit 20 times, we expect he would "give up" about 4.6 hits and 8.4 total bases that he might have gotten had he swung away. (I assume there would be no effect on his walk rate--redo the calculation if you disagree.) Thus, his BA and OBP would remain the same if he was successful at bunting for a hit 23% of the time. His Slugging would be unchanged if he were successful 42% of the time. His OPS would be unchanged if he were successful about 32% of the time.
If, on the other hand, he was successful 40% of the time (less than league average) with 8 hits, then his BA would go up by .006, his OBP would increase by .005, his slugging would go down by .0007, and his OPS would go up by about .004. These are very small changes and unlikely to induce opponents to stop shifting against him.
Now, let's look at the effects of the shift. We do not know what Rizzo's "natural" BABIP is, and won't know for another couple of years. But I would think it would be greater than .258. Assume his "natural" BABIP is .290. Then, his reduced BABIP resulted in the loss of about 15 hits in 2013 (.032 x 458 balls in play). Perhaps this was all luck. But opponents shift because they believe it will reduce his BABIP. If all of the .032 shortfall in BABIP was due to the shift, that is 15 hits a year. Even if these were all singles, recovering those 15 hits would raise Rizzo's BA by .025, his OBP by .022, his SA by .025 and his OPS by .047. That is rather significant. The potential gain is sufficiently large to make it worthwhile for Rizzo to bunt for a hit a lot more than 20 times a year, provided he can maintain a 40% success rate. Eventually, opponents will stop using an extreme overshift and Rizzo's results would benefit from the increased BABIP.