I disagree about 95% with this.
The flatter USPS PM boxes are THIN. They don't even have an edge compression strength, they are so thin (yeah there is a number no doubt but they make 0 claim to it, what does that tell you?). So to be clear I am not talking about the more cubic shaped ones, those are pretty heavy duty, but don't really fit most Lego boxes that well.
So sliding a set for which condition is important into a nice close-fitting flat free USPS PM box, no matter how you wrap the thing (unless wrapping it in a cardboard type "shell" that will substitute as a second box vs. compression) will not protect it from the normal wear and tear of being handled, stacked, gently tossed, dropped, let alone any real abuse. And the tighter you pack it, the easier it is for it to get damaged due to compression. In fact, a stronger box with more dead space above and below the set is better, because compression is going to happen no matter what. Bubble wrap and most filler are only good for keeping a Lego box from clattering around and sustaining minor corner / edge damage in a box that is significantly bigger. Think about the trucks, guys. Your little 16x10x3 Lego set could be near the bottom of a 10' high stack of packages weighing hundreds of pounds, rocking back and forth for hours, hopping up and down across dirt roads, speed bumps, potholes, curbs, wildlife, whatever the case may be. That box is going to yield - and we all know there is plenty of space inside the Lego box, so guess what? once the outer box touches the Lego box, the force is transmitted to the Lego box and the item starts to become damaged. Common scenario is when a heavier, smaller box is put on top of these flat PM boxes, and the edge of the heavy box nearest the weaker middle section of your box grinds it's way down into both the PM cardboard and the Lego set over time. Bubble wrap and packing paper won't do anything significant to prevent this.
I worked in a UPS hub as a package unloader for a year in college. I am a collector of very nice condition Lego sets, with 7 years experience analyzing hundreds of packaging jobs from other sellers, about 2/3 of which have been inadequate, and about half of those got away with it, through dumb luck... and I sell to all kinds of customers - those who care about condition and those who don't. The ones who do care have been seriously impressed with how I protect their purchase. I see it from all angles, and I'm telling you:
DON'T USE FREE FLAT USPS PM BOXES IF YOU NEED TO REALLY PROTECT A SET.