I think you'll find that a majority of F-Open shooters turn necks, whereas some F-TR shooters using .223 Rem or .308 Win turn necks, but plenty do not. Nonetheless, the use of a mandrel as the final sizing step may offer some benefit to your reloading regimen. It's not an endeavor requiring a huge expense, so it might be worthwhile to give it a try before committing to turning all your necks, just to see whether it helps.
There is a potential downside to the type S die expander ball that expands the neck as it is pulled [out]. I have observed a number of occasions where people had runout issues that ultimately were found to result from the expander ball. I remove the expander ball before use on all my type S dies. You will need to empirically determine whether you die setups with the expander ball induce runout. If not, that may be all you need.
One of the keys to purchasing the correct sizes of bushing or mandrels to re-size necks is being aware that the spring-back of the brass works in the opposite direction. In other words, a bushing squeezes the neck down, so the neck will open up slightly after it comes out of the die, whereas a mandrel opens the neck up from the inside, so the neck will shrink slightly after the mandrel is removed. In either case, it is usually necessary to move the brass a measurable amount. Trying to use either approach where the selected size bushing or mandrel is almost the exact same size as the neck diameter already is does not give consistent results in my hands. In the most common use of a bushing die, that is rarely an issue because you're using it to squeeze down the necks of fired brass that will already be several thousandths larger than the chosen (desired) bushing. Thus, the brass is being sized a noticeable amount and the bushing can do its job efficiently and effectively.
If you decide to use a mandrel as the final sizing step with fired brass, it is obviously necessary to size first down the necks of fired brass to a diameter at least .001" to .002"
smaller than the mandrel will ultimately open them up in order for it to do its job effectively. Some testing/experimentation may be necessary to determine the correct bushing to allow the mandrel to do its job, while not excessively working the brass.
Once that is done, I think you will find that the proper use of a mandrel as the final neck-sizing step can provide very uniform neck diameter and neck tension (interference fit), as well as very straight necks (i.e. little to no runout). In my hands, a mandrel that is approximately 0.0015"
under bullet diameter will give very close to .002" neck tension. Again, that is because of the direction of spring-back when opening necks up with a mandrel is for them to shrink a tiny bit. This is because you first sized them with the bushing die to a slightly smaller diameter in order to allow the mandrel to effectively open them back up to the final desired diameter. A mandrel that is a full .002" under bullet diameter will usually give somewhere in the neighborhood of .0025 to .003" neck tension for the same reason.
There are different options for use as mandrels such as the calibrated pin gauge sets, or mandrels made specifically for re-sizing cases. For a number of reasons, I prefer the 21st Century mandrels. More specifically, I do not need a particularly wide range of sizes as I already know pretty closely what size I need for the job (i.e. a mandrel .0015" under bullet diameter gives very close to the ~.002" neck tension I typically use). They are a bit more expensive than the pin gauges, but they do not require any further modification for their use. Here is a link to the 21st Century mandrels and die:
http://www.xxicsi.com/expander-die-body.html
http://www.xxicsi.com/caliber-specific-expander-mandrels.html
I also keep a few other sizes of these mandrels around for specific tasks, such as removing "flat spots" from the necks of cases fired in rifles that have strong ejector springs. Whenever I need a new size, I purchase it and add it to the set.
Another consideration for the use of mandrels to size necks I should note is that my F-TR rifles all have no-turn neck chambers. Thus there is plenty of clearance between the chamber and the case neck wall. The idea of using a mandrel to size necks is that it will push some of any non-consistent neck wall thickness to the
outside, thereby providing better and more uniform neck tension and seating force. However, it may not work as well in a tight neck chamber intended for neck-turned brass if there is not sufficient room for the neck walls of unturned brass expanded with a mandrel (i.e. some of the inconsistent neck wall thickness pushed to the outside of the neck). The reason for this is that the bullet of a loaded round is essentially self-centering with respect to the bore in the long tight freebores we typically use in F-Class rifles if there is sufficient clearance around the case neck. If you have even a moderately tight-necked chamber, you may have better results just going straight to neck turning. Nonetheless, the use of a mandrel is a relatively inexpensive option to consider for improving consistency of neck tension.