The volume of metal increases by a factor of pi as the diameter increases
While that's not exactly mathematically correct, the important points are very true. More metal in the shaft means more rigidity, more momentum, and more dampening - not unimportant, as the cutting force initiates a lot of vibrations, in all sorts of directions. More mass means more dampening of these forces, and more stiffness means less "give" to begin with, so the amplitude of the vibrations are smaller to start with. ( sadly enough, there is an inverse relationship between stiffness and dampening, but in the end, "more metal / mass" wins hands down ).
Less vibrations and less give mean cleaner cuts - that's a good thing.
So why don't we all use 1" shank router bits? Well, there's other trade-offs.
First of all the weight of the tool. Spinning up and spinning down a large spindle ( you want your spindle to be larger then the diameter of the toolshank from an engineering point of view ) means more energy lost in spinning up and slowing down the spindle. From an energy standpoint this may not be dramatic, but it takes time, and strain on the motor. Lots of Festool routers use an electronic braking system, very useful. But braking larger masses puts more strain on the system, burns brushes faster in universal motors ( as does spinup ) so in general should be avoided.
And while a decent mass may feel stable in you hands it will wear you down in handheld use - and besides: the larger gyroscopic forces may make it a lot less controllable, however stable it feels. Corrections are far more difficult when using a large spinning mass. Imagine a trim router with the gyroscopic force of a big 3hp router. The smaller the spinning mass, the easier it is to control. If you can't grasp this: take any router ( unplunged for safety ), spin it up in free air, and try to make figure 8's with any of the handles. The counterforces you notice are directly proportional to speed and MASS of the spinning parts.
There's also the small issue of radii. For a 1/8" straight flute bit to be of any useful length, a 1" shank would be far from optimal. For the force distribution to be optimal in the tool, the radii in the profile ( for diameter reduction ) should not be too small, otherwise the bit would be prone to breakage. Shallow bends with a large radius as well as slow tapers to overcome the diameter difference will prove stronger than acute steps with small radii. So to make a 1/8" straight bit on a 1" shank would most probably take at least 1/2" of length from the shank to the cutting part. Which means more stickout from the collet, equalling more vibration, etc, etc.
Besides, Any counterforce from a vibrating bit would not be able to counteract the enormous mass of the spinning spindle, so a "suboptimal cut" that might just be "communicated" to you by a lighter router will probably snap the bit in an instance in a heavier system, most likely ruining the workpiece.
So as simple as it may seem, there's always a tradeoff. Here in Europe, most people seem to feel that the 8mm bits are a very nice compromise for lots of bits. Whenever 8mm starts to loose it's merits, we do 12mm or 1/2", both are available. You'll be hard pressed to source any 1/4" bits around here. A long time ago, B&D have tried to spawn interest in 6mm bits ( just under 1/4" ) but it never caught on, and the idea died a merciful death (Smaller still, there's Dremel with it's 1/8" shanks).
In case the 12mm or 1/2" won't suffice: go shaper.
Regards,
Job