And just because we're discussing lever movement in general, we really need to discuss/define what 'free play' means.....
Free play is the sum of all of the 'slop' in the system, as measured at whatever point of reference you want to use. With levers that's typically relative to the outermost point on the lever, and usually describes the wasted range before the lever starts doing what you want it to do. This number has a specific value when there is a cable involved, and a MUCH smaller one, when the lever is operating a hydraulic control. I'll go into that another time, we're only talking about the front brake lever in this case. Considering I've ridden bikes with cable operated drum front brakes through every generation of disc brake design...... there's a TINY amount of free play in current radial front brake designs. Practically zero.
The biggest advantage of the latest generation brake system designs is the very limited number of variables that remain. It's a similar situation to shim under bucket valve actuation; there are the least number possible moving parts.
In the case of the valves, it's just the cam pushing on the bucket (with the shim for adjustment underneath) and the springs to pull the valve back out of the cylinder. All of the motion on the valve is delivered in a purely vertical direction, because of how wide and solidly supported the bucket is that the cam is acting upon. No lateral motion involved. A piston in comparison has significantly more lateral force.
With the braking system, the radial MC has fundamentally changed how the plunger is moved to provide the force to the calipers. Earlier designs used a cantilevered system to push on the plunger, so the force applied was similar to what happens on the rear suspension with the linkage..... not linear. Every pivoting part has to have some clearance, so that it can move. Every moving part adds to the stacking tolerance of the entire system (the total 'slop'). Every lost motion in the movement of the control, is magnified by the mechanical advantage the lever is using to act on the pistons in the caliper. If there's any flex in any of those parts, it adds to the 'rubbery' feel..... if the brake lines are weak and can expand under pressure.... even more 'rubbery'.
If there is any moisture or air in the lines.... the moisture turns into steam when heated, both air and steam are compressible.... which feels 'rubbery' as well. Moisture is a particular concern because of how much more volume steam occupies compared to water..... on the order of 1,000 times more volume. Good seals and fresh fluid from a sealed container are critical when servicing brakes. Once the seal on the brake fluid is broken, the clock starts ticking. Shit can your left over fluid. Saving it for later use is a false economy.
With the radial MC the plunger acts directly on the shaft connected to the plunger, as the orientation of everything has been changed so that the lever pivot is 'outside' the arc that the shaft moves through to actuate the MC piston. It's a straight shot without any changes of direction, or lateral motion. It was initially more difficult to manufacture (and as a result more costly), but that's now a moot point as the advantage is so clear cut. (previous designs had legacy to those cable operated drum systems at some point in their past.)
Radial calipers are an incremental improvement on the preceding caliper designs, in that the friction material is more closely aligned with the rotation of the disc it acts on. The more important aspects of the caliper's design relate to how structurally rigid they are and how much of the force applied form the MC is applied directly to the pistons pushing the pads into the rotor. Single piston, sliding pin calipers gave way to double piston calipers, gave way to 4 and 6 pot designs, which sought ever better 'feel' and repeatability/sustained stable use.
Initial 'bite' occurs when the pad first engages the rotor, and rolls into the rotor due to the friction. The leading edge of the pad makes contact first, and depending on how hard you apply the brakes may remain as the primary contact point. Multiple pads in the caliper came about to expand on that 'bite'. More pads, more edges, more 'bite' area. Different sized pistons in the caliper came about, to try and eke out as much of that 'bite' as possible.
All of that 'feel' is lost, if the caliper body can flex, or the mounts are loose, or the fluid is saturated with water, or there is grunge making the pistons stick in their bores (that changes the distribution of force), the rotors are warped, the lines are weak, or something is wrong at the MC.
Everything I've discussed relies on the pads being a very small distance from the rotors when not actively being applied. If that distance is changing, it will result in a change in the distance the lever has to travel to make the pistons move to make the pads engage the rotor.
I cannot think of a reason for the gap between pad and rotor to be greater than the smallest measured value, for ANY pad/rotor measurement. The pads should skim just above the rotors, without making contact. I'd bet the intended gap is less than a human hair.