@MikeD has talked about this before, but a modern transport category jet does not have a cockpit that is designed for see and avoid. On both the 32X and the 330, at the speeds that we fly in the terminal area, I can reasonably "see" just a bit of the airspace directly in front of me. In a turn or change of altitude, that area decreases even more. That's one of the problems with operating a transport jet in non radar, uncontrolled airspace. You can do it just fine, but the risk equation drastically increases.
The risk equation indeed increases, and the only thing you can do is the best you can with your limitations. Even with todays traffic safety systems, there may be uncontrolled fields you’re going in and out of where some GA may have no transponder, negating TCAS or TIS/TAS systems protections, and may also be making inaccurate radio position calls or even none at all. That leaves accurate and timely position calls on our end, and seeing and avoiding to the best of our cockpit view limitations (737 isn’t much better than the Airbii), as all we have. Which indeed ups the risk.