The drawbacks that I experienced are:
1. It takes relatively twice as long to do everything. Instead of making one pass over two blanks (turning, sanding, or finishing), you make one, then change blanks, then do it all again.
2. Because each blank is turned, sanded, and finished separately, the 2 ends are more likely to turn out different than if they are mounted on a mandrel where you can see and monitor progress of both blanks at the same time.
3. You have a very small area of clearance for the tools and for the paper towels or shop cloths used in finishing.
4. Unless you can afford to buy custom made bushings, there is no good way to turn or finish 7mm tubed pens without a mandrel.
I do sometimes use the mandrel-less system when I'm making Sierras, and also sometimes for finishing up Cigars, Barons or Sedonas, etc. To me, the system has its uses, but it's not a "one-stop" solution.
There are some people who will vehemently disagree with everything that I said about the disadvantages, and they may be right. You just have to experiment with it and see if it works for you.