If I was trying to do what you are proposing, I would use a
long-reach booklet stapler (click the link to see an example.) I have the Swingline version here in my office for creating booklets and binding ebook printouts that are too small for glue binding.
In the late 1990's I was in charge of producing and distributing a large quarterly fundraising newsletter. We printed on tabloid size paper and created an 8 page newsletter which was delivered via the USPS. The printing was done with a
high-speed Risograph printer and the binding was done with 2 staplers that were identical to the ones I use today (I mounted them side-by-side on a board and rigged a bar across them so I could place 2 staples at the same time.)
The jig I made for the staplers made lining up the pages and binding them an easy process. So, I would set up a mini assembly-line with my printed pages at one end and a box for the bound, folded newsletters at the other end. Then, I would put a video on the TV, pour myself a refreshing beverage, and bind the night away - happy memories!!!
If you are doing high volumes, there are automated (and expensive) options. You can also have the binding done at your local copy shop. But low-tech give very professional results here.
Andrew