Hello,
I have no experience of these mini routers, but I am doubtful that they would have enough power to do what you are suggesting, up to 50 times a day. In industry today, I expect they would be produced on automatic lathes, or CNC routers. In the past they would probably be produced using an overhead router, such as a Wadkin LS. Using appropriate jigs. (Used mine today, only to cut plastic tho!)
Handheld woodworking routers run at around 20,000 rpm, and are rated at around 1000-2000 watts. I use a 2000 watt router, with ½ inch cutter, ½ inch depth of cut to rout softwood staircase strings. In hardwood ¼ inch depth of cut is more comfortable. The downside of routers are noise and dust. The dust goes everywhere, as Frances said, and the high pitched noise, annoys everyone.
As HowardT said, a handheld router inverted in a table, and suitable jigs would do what you want, Bandsawing first will save a lot of strain and dust, and will mean you only need one pass around the outside. Both MDF and softwood will leave you a sanding challenge.
Using real wood, will mean routing against the grain, in two of the four quarters, leaving a rough finish, the less close grained your timber, the worse it will be. Sanding the edges of MDF is tricky, as the fibre ends tend to flick back and forth as you sand, it's a bit like sanding the bristles on a scrubbing brush!!
Turning the blanks on a lathe, would allow for sanding the edges at the same time.
You also have to work out how to hold your blank, whatever machine you use, as you are machining through 360 degrees, clamps are a nuisance. You can use a couple of wood screws, if the holes don't matter, otherwise you are into vacuum chucks, and more expense.
Wadkin LS
Wadkin LS Operating Guide
The operating guide, probably from the 1950's or 60's, has lots of information on jigs etc, including Tap and Die box making, my favourites are the jigs for spectacles.
Mark.