Not all poly-foam is the same. From the picture shown, I would also most hazard a guess that the poly-foam was actually designed for pheasant and not chicken eggs. Back when I did bobs and cortunix on a regular basis, I used poly-foam BUT (notice the capitals there) I also used the upper and lower panels which were at least 3/4 inch deep. I would make two cardboard panels the same size of my poly-foam and create a cardboard, padding panel, poly-foam crate, padding panel, and cardboard sandwich. This was then wrapped in a newspaper folded up just so to make a lift out handle on it. I'd layer packing stuff, usually wadded newspaper or a newspaper/peanut blend, on the bottom of the box. Pop in the newspaper wrapped poly-foam egg sandwich, stuff more paper around the sides, and then newspaper or newspaper/peanut blend the top. Doing the blend gave me a chance to recycle peanuts that others would use to ship to me. Considering I shipped off 1000 bob eggs (with extras it came to 1,079) from Central Texas to Tacoma, Washington one time using this method and the guy called me 4 weeks later asking me what the heck happened with the 14 eggs that did not hatch, it makes it hard to blame poly-foam.
Now, I have also received eggs packed down in shavings and paper-mache cartons, those thin styrofoam cartons like at the grocery store, bubble wrapped, double bubble wrapped, paper towel wrapped, and even ziplock bags that have had great hatch rates. Eggs I've gotten with poly-foam and all these other methods, I have had crappy hatch rates. Distance hasn't been a factor either. Neither has heat and time in the mail truck. I have received boxes that are pristine, without any indication the post office touched it except for the post mark with little to no success in hatching and those that look like they were used for a rugby match and had to improvise brooder boxes out of boot boxes and night lights since even the extras decided to hatch. I can't even chalk up a successful hatch to my incubation since I've had crappy hatches in a Sportsman and 100% hatches in one of those little stupid yellow salad bowls from GQF.
This places the problem with hatch rates within the realm of the post office or the breeder. If the birds are not fed a good quality feed when they lay the eggs, you wind up with embryos that may not have that desire to thrive. If the eggs are saved up and then shipped out, if they haven't been stored properly, you have an egg that had already started the incubation process when shipped or an embryo that got way too cold. If the package went through extremes of heat and cold and bounced around like a 3-year-old on a trampoline after consuming their body weight in sugar, it would be a good guess that only the fittest will make it through the incubator and brooder to wind up in the coop. Translation: shipped eggs are a coin flip when it comes to winding up with the amount of birds you want, you have no choice but to take your chances.
All that being said, there is a trick to getting eggs out of the polyfoam. If your eggs do not come with the sandwich process and a lift kit to get them out of the box, DO NOT take the darn crate out of the box. Take off any and all covering to get to the actual crate. Slowly work a hand under one corner of the polyfoam while angling towards the corner egg. Once you get where you can feel that egg with a finger, any finger will do, take the other hand and place it gently over the egg, applying just enough pressure to the polyfoam to make a dent in it with your fingers. Slowly poke the egg up from underneath. The combination of upward pressure from your finger and downward pressure on the foam will cause the egg to rise up. Once it clears it's widest diameter, stop poking from the bottom (you will feel a decrease in resistance with the bottom hand when this happens). Close the fingers on the other hand around the egg and put the egg in the "secure after shipping resting place". Repeat with the rest of the eggs. The hardest one to get out will always be the first one.