A possible partial explanation (Long and detailed, maybe even boring))
I worked for about 30 years as an executive in the printing industry in book, magazine and catalog manufacturing. (I have been retired for about 8 years, but I retired early so I'm still young

)
Distribution of these printed products can be troublesome and expensive. I'll tell you a little about how magazines are distributed books and catalogs have their own idiosyncrosies.
I don't know all of the capabilities of Ovid Bell Press in Fulton, MO, who prints AMERICAN WOODTURNER, but from the quality of the three issues that I have seen as a subscriber, I would say that they are a high end manufacturer. (I still don't have my copy yet and I'm only a few hundred miles from the printer.) A quick Google search found a web site that gives a brief description of their capability. They appear to specialize in magazines and related products. Because of this they, of necessity, are also in the distribution business for these products.
The membership of the AAW is about 10,000. Therefore the print order is probably less than 15,000. With today's high speed manufacturing this is not a long run, either in the press room or in the bindery. The printer wants to get the job in and out as fast as he can so he can bill the job. Therefore, these publications don't stand around very long at the printer. The only storage the printer might have would be for the back issue copies for future use (AAW might even warehouse their own back issues).
Now, to address the distribution situation.
MAILING DISTRIBUTION
While these magazines are being saddle stitched they are also getting the name and address ink jet labeled. They do this electronically with data supplied by the AAW. The list is also pre-sorted by postal requirements for the maximum discount on the postage bill that AAW has to pay. The finer the sorting, the bigger the discount. As the magazines are being stitched, labeled and trimmed they are separated for postal sorting. The top line of the label on my magazine has ALL FOR ADC 720. My zip is 72401 so mine goes into a mail bag that gets a bag tag label, data also supplied by AAW, that is attached to the bag and when all of the magazines destined for 72XXX are in the bag, the bag is closed and put on a pallet that is destined for a USPS facility that will further re-distribute the bag. Sometimes the pallet loads go to more than one postal facility to be further reshipped either by over the road truck, plane or train until it gets to the post office that services the subscriber. There the letter carrier that will sort all of their mail and when they get into their truck will proceed to take AMERICAN WOODTURNER home with him/her and when they are finished reading it, they will deliver it to you.

(I doubt that any of them do this.) Magazine mail does not hang around the printer very long or they would be inundated with this and other magazines, and as I mentioned before, they want to bill the job as soon as all of the direct labor in done. The timing for mail delivery is completely at the control of the USPS.
(There is a whole industry that tracks mail delivery with sometimes pretty sophisticated delivery checking methods. Catalog delivery in the mail is often critical to time with store sales, but that is another story.)
NEWSSTAND DISTRIBUTION
The copies of the magazines destined for the newsstand do not get a label but are sorted into packages of varying quantities according to the resellerseller requirements. These usually, but not always, are sent to a magazine distribution company that can distribute cost effectively because they group magazines from a number of printers that are sending magazines to the same reseller locations. Most often these are sent out from the magazine distribution company by over the road truck and these companies are pretty efficient. They arrive at various cities and are futher redistributed to the reseller, along with a number of other magazines. These companies don't want to warehouse these magazines so they need to get them to the reseller as fast as possible, in keeping with the magazine's "on sale" date.
There are a number of marketing strategies involved in magazine newsstand selling but these are usually limited to magazines that have print quantities in the hunderds of thousands.
CONCLUSION
This is the normal way that most magazines are distributed. It is also the most cost efficient way, overall.
If the AAW were to mail some copies by first class mail it would probably require a special addition to the above distribution scheme. This means that some of these magazines would likely have to be put into an envelope, of some sort, labeled and have postage applied. For most printers this would be an off line operation because of the small number of copies involved. It also is likely that it would be a hand operation, as opposed to a high speed machine operation. Whenever hand operations are involved it usually means additional expense. The first class postage would also be more than 2nd class publication postage. However, the postage could be the least expensive part of mailing a magazine by first class mail.
DISCLAIMER
This information is from the deep recesses of my memory and is at least 8 years old. I am not in any way involved with Ovid Bell Press. I am NOT an AAW spokesman and I only share this information of my own volition for those who might want to understand a little about the distribution process. (The printing manufacturing process is much more interesting than distribution. Sort of like turning is more interesting than the finishing, for some people, but it must all get done to be completed correctly. The AAW has to have the USPS do some of the finishing.) Specific systems and processes might (probably) have changed since I retired from the printing industry but the general principle would be the same.
Clem