Well first, there is a clear difference between paying a premium for everyday position players/starting pitchers & relievers.
Second, for the White Sox, it kind of makes sense to overpay for a reliever because they're trying to make a deep playoff run and the rest of their team is looking relatively complete. Let's try spending our money on actual holes such as CF, INF, SP instead of spending $13.5M/AAV on a high end reliever, which is one of the last pieces we really need. This front office picked up Anthony Bass from the waiver wire and Rafael Dolis from Japan just last year and always have had moderate success building at least average bullpens. It's never been a problem for them.