We often do that too, after a quick visual check looking for tombstoned parts and other obvious flaws. (You have to do that anyway, because tombstoned bypass caps can lead to flaky failures.)
Finding dry solder joints and so on can be time-consuming, and they can cause overstress to other parts when the board gets powered up. Plus (like you folks) our BOM cost is a smallish fraction of the price.
I have a set of Smart Tweezers that I use for looking at parts in-circuit and for testing e.g. random electrolytics from the drawer that I'm putting in a proto. Not cheap but pretty good. That's about the only time I need to test ESR.
Re: beta
Beta distributions for a given type are sometimes annoyingly tight--I can't get plain BCX71s, for instance, and the suffixes are a moving target--they're al the way up to K now. Design in a BCX71G, and you find you can't get them anymore. Even the Js are getting scarce.
Cheers
Phil Hobbs