In a world with perfectly flat records and platters with no resonance, clamps and mats probably wouldn't be necessary and, as Dougdeacon points out, might even be counterproductive. On both my Music Hall MMF-2.1 and my Thorens TD 150 the platters were ringy enough to need a mat and some of my records have warp enough to need a clamp. On my current Well Tempered, the acrylic platter works great without a mat, and has a slight dish along with with a screw clamp to tightly couple even a flat record.
Clamps are definitely an area where you'll get no consensus among manufacturers OR audiophiles.