FWIW, my last trip to St Anton was the first season that the Flexenbahn was open, and I didn't have any problems with crowds or bottlenecks. That said, it was mid-January, not school holiday time, so crowds weren't really an issue in any part of the area. Also, snow conditions were excellent, so I was able to pop off the piste on the downward leg towards Zuers.
For me, the biggest hassle in the Arlberg area is getting from Zuers to Lech. I always end up on a scraped-down, icy ski route that bottlenecks into a flat spot, so it can be difficult finding enough space to build up the speed necessary to avoid skating/poling my way to the one lift heading towards Lech.