I am always skeptical of arguments like this. I think we as fans tend to overrate things like intangibles. Look at Vontaze Burfict. Dude is a Grade A @#$%&, yet he is still a key piece for the Bengals.
Because we aren't usually skilled enough to understand details about what a player does well and poorly, and how that aligns with a coach's goal scheme-wise, it's difficult for us to understand decisions like Britt v Woods on anything other than the levels of production and public-facing personality.
I'm not saying you're wrong about McVay pursuing character guys, and it DOES seem like Woods beats Britt in that area. But I think the reality of the NFL is that things like scheme fit play a much bigger role in these decisions than the other factors that we usually exaggerate in our heads.
In the end, all that matters is winning.