I had a LaserFibre drop weight table-top machine as my first rig (US version of Stringway) that included floating clamps. Although it was technically a 4-point mount, those points were right next to each other at 12 and 6 o'clock with no support for the sides of the racquet hoop.
It never occurred to me that this minimal mounting was any sort of issue until one day when I was stringing an older Volkl C10 at perhaps 62 lbs. After finishing the mains, I had a few of the crosses done when I looked down at the hoop with the next cross under tension. Although the frame wasn't cracked, it was significantly deformed by that applied tension - it's shape went back toward "normal" when I released the tensioner.
My C10's (both old and newer) were significantly softer through the hoop than my previous players - the rock-solid Wilson ProStaff 6.1 Classics. I certainly understood that installing the strings, especially the crosses, creates a bit of an imbalance in terms of load, stress, etc. until all the crosses are done, but that degree of deformation was an eye-opener for me. After seeing how "bent" the unsupported hoop of a softer racquet could become during stringing, I knew that I'd be shopping for a six-point mounting scheme in my next machine.
Now I have a six-point Gamma Prog. II ELS, which has been ideal for me and completely issue free for well over six years. What has occurred to me since I got this machine is that it's less stressful on racquets during re-strings in two ways. I already covered the aspect of having more support available for the hoop during string installation - much less deformation potential.
This newer machine is also less stressful for racquets than my older rig because its fixed clamps have less inherent drawback than the floating clamps on my old machine (which was also constant pull). I quickly discovered that I needed to set the tensioner on the Gamma at 4-5 lbs. lower tension than I did with the LF machine to get the same final firmness in a string job. So the fixed clamps let me hang less stressful tension on each portion of string to get the same result. Double bonus points... or something.
Two-point mounting can certainly work, but if it comes down to a few hundred extra bucks for a machine that I plan to use for many years, I have a lot more confidence with six-point mounting as well as fixed clamps.