I don't know why a wrestler would step on the mat and fake a match to purposely lose when they could simply default.
With that said, the question is, do we want the best 4 wrestlers to advance and represent the district, or do we want the 4 wrestlers that a randomized bracket produces? If we truly want the 4 best (most deserving) wrestlers, you have a true 4th round. The round might add 20-30 minutes to a tournament tops. If a true 4th isn't offered, coaches and wrestlers will forever attempt to do what they think is best in order to get into the top 4. The system is flawed and unless its fixed, this will continue. I'll give you a very specific example and I could point out plenty of times this happens, but here is a specific one from this weekend.
SW DI Kettering Fairmont District - 120lbs.
Springboro wrestler finishes with a 4-2 record. He lost to the 2nd & 3rd place finisher.
Hamilton wrestler also finishes 4-2. He lost to the 3rd place finisher AND head to head to the Springboro wrestler via a 12-4 major decision. However, because of the random bracket placement, the Hamilton wrestler advances to state, while the Springboro wrestler does not.
If you don't see the problem with that, I don't know what to tell you.