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Top-loaders added to a stiff mailer like that will have a good chance of creating a non-machinable mailing. First class letters travel through a slalom course of rollers, spindles, belts and flippers while being sorted into different cubbies. They need to be flexible enough to bend around the curves. And the problem is that each major center may have different sorting machinery with different levels of sensitivity to jamming, so clerks at different post offices may have differing experiences with rejected mail pieces.
Look closely at the edge detail of the mailer you chose. There are three layers of cardstock on the edge seam making up 2mm of stiffness. The mailer weight is 30 grams. Fat or abrupt edges can become a big problem.
My method (below) is only 1mm of protection at the seam, weighing 14 grams, and thus is half as stiff as yours. That probably means it is half as likely to withstand folding, so the judgement call is yours. You can use this as an example of the flexibility required to avoid jamming and to avoid a non-machinable charge.
In my example I tape the clear sleeves to the folder to maintain separation and to also prevent the contents from shifting, falling into the seams where they can cut their way out, or doubling-up on each other.
Here is one end of a typical sorting machine. Can you see the white blurs that are letters whipping around corners, belts, and spindles? They travel at such high speeds that they really are only a blur.
Below is an older sorting system with a letter feeder that flips out letters that are too thick or that approach wrong. Below that, there are flippers that direct traffic. You can see the sharp bend required within the first inch of the letter (lower image).
