Milling machines need a lot of rigidity to avoid not only imprecision but even oscillation, or even grabbing in the case of climb milling, under the heavy side forces created by their cutters. Their workholding setups also must withstand these side forces.
The cutters are most commonly end mills doing side cutting. It occurs to me that, when doing a straight cut while side cutting, if you have two counter-rotating end mills close to one another, so that one is climb-milling while the other is conventional-milling, then only the spacing between the cutters needs to be rigid to resist the cutting forces, because the forward force by one cutter can be balanced against the reverse force by the other cutter. By adjusting the two cutters’ engagement depths and spindle speeds, you can use a controlled imbalance in these side loads to feed the machine through the material, eliminating the need for a high-power feed motor driving the X and/or Y axis; the feed motor only needs to oppose the side loads perpendicular to the toolpath, which will be only partly canceled by this setup but do not require any power, just holding.
The two spindles might be mounted a fixed distance apart on a small turntable rotating around a C axis, for example.
Of course you need active feedback to monitor the resulting positions and feedrates and adjust the angles and spindle speeds between the two cutters to compensate.
Doing this for more complex surfaces might require rotating the carrier for the two cutters around two axes, not just one. If the cutters are not ball-nose endmills, it might then be necessary to rotate the spindles back to verticality.
In face milling, it should be possible to do something similar most of the time while cutting almost twice the width of a single face-milling cutter in a single pass, by overlapping the paths of the cutters slightly, while overlapping the path of the leading cutter with a corresponding amount that was cut in the previous pass. That same overlap will create an imbalance between forward and backward forces which can enable the cutting forces to feed the cutter into the material.
To do the same kind of thing for single-point cutting on a lathe, you could use two cutters on opposite sides of the workpiece, perhaps with a negative rake angle on them so that if one strays a bit closer to the center of the material than the other, the cutting force will push it back out, so that the cut is the same depth on both sides. Using three cutting points instead of two eliminates an undesired degree of freedom in movement.
This is pretty much the same way that dies, taps, and countersinks center themselves on existing round features, and drills follow existing holes, so it could lead to cutting non-concentric features. If the cutters’ rake angle can be varied dynamically during each revolution, you could use position feedback to cut deeper on the high side and thus recenter the cutting; a system of levers referenced to the desired cutting axis can achieve this. The same approach can be used in place of a boring bar: a sort of hole-expanding drill or boring head that self-centers on the desired cutting axis by changing the rake angles of its cutting points.
These drilling-like approaches surely eliminate most of the usual side forces and workholding forces: if you’re cutting a vertical cylinder, inside or outside, then all the horizontal cutting forces cancel between the three cutting teeth. It’s like a drill press: you still need potentially a vertical force to feed into the stock (and to hold the stock in place as you do that), which maybe you can avoid by tilting the teeth forward or back to pull it into the stock at an appropriate speed.
But the bigger remaining issue is that the moment from rotating the teeth relative to the workpiece is still present; this is what potentially causes a poorly held workpiece in a drill press to spin around on the drillbit and break your hand. If you’re cutting on a large radius, this moment is potentially very large, and it needs to be resisted (probably quite rigidly) across the whole workpiece-workholding-frame-spindle chain. If instead of using three rotating teeth you use four rotating endmills with steep enough helices to ensure continuous contact, then this problem can be eliminated; two of the endmills can rotate in one direction while the others rotate opposite them, with the relative depths of engagement determining the overall revolution of the assembly. It might be possible to reduce this to two endmills and a roller.
Using ordinary endmills would give up the ability to control the rake angle, but a more elaborate endmill design with movable inserts could retain that degree of control as well.
For face milling, the equivalent of concentricity is tramming. You could imagine a sort of three-pointed fly cutter which dynamically adjusts the rake angles of its three teeth as it moves over the surface so as to cut deeper on one side than the other, in order to bring the surface into parallelism with the desired plane. If we suppose the surface is horizontal, the cutter’s yaw axis is driven by a spindle, while its pitch and roll axes are controlled by its engagement with the surface. Some kind of force is needed in Z to get the teeth to dig into the stock (unless a steep rake can provide that force on its own). The varying degrees of engagement produce side forces in X and Y, which will not in general correspond with the desired direction of motion across the workpiece, so X and Y feed motors are also needed.
If instead of one three-pointed fly cutter we have three, the X and Y side forces from the nine points can be controlled to provide the desired X and Y feed.