Not to belabor the point...BUT:

Let's say you have a tail swap, and due to inbound delays, the crew taking your airplane is not there yet. On landing, one of your two nosegear tires went flat. Since you evidently aren't required to do a postflight inspection, you continue about your business and unknowingly leave the airplane sitting with a flat nose tire.

Next crew shows up 30 minutes later, and once the preflight begins the FO immediately notices a flat nose tire. Now, the already delayed flight is delayed even longer as maintenance is called to swap out both nose tires and get the airplane airworthy again.

This additional delay could have been vastly reduced if the flat had been discovered on a postflight inspection, and the crew who brought the airplane in wrote the flat up and called it in to maintenance control for repair. Now, lets replace flat tire with "engine oil leak", "hydraulic leak", "tailstrike", or any other number of problems that a quick runaround would have discovered - see the potential problems such a policy exposes your crew and company to?

When I was at AWAC, the only time I wouldn't postflight (even in the crappiest of weather) was if the crew taking the airplane was RIGHT THERE upon our arrival and I knew the FO would start the walkaround immediately.

Again, not bashing on you...just how the company has set their operation up for operational problems via policy (or lack thereof).