Yes and no.
Increasing the free travel delays unlocking, but you also get higher bolt velocity for the same amount of gas. Higher bolt velocity brings with it its own set of extraction and cycling issues. So, an increase in free run before unlocking may make the system more sensitive to port pressures outside the design assumptions.
The whole system is, well.... a system. Changing one parameter of the system cannot fix all possible problems. The AR system was designed around a rifle length gas tube, so that is where it will work best. Changing the length of the gas tube introduces problems that can be addressed in various ways, and each proposed "fix" will introduce other limitations, or problems. Sometimes the new limitations or problems are less severe or easier to live with, and sometimes they are just moving the problem from "here" to "there".
This problem was described once to me with "The balloon in a box" analogy. Image the AR-15 with a rifle length gas system is a balloon in a box, both of which have the exact same volume. The balloon can be placed in the box and the lid closed and it fits. Now, the carbine length gas system is a box with a slightly smaller volume, but the balloon is still the same volume as before. Now, when the balloon is put in the box and you try to close the lid, part of the balloon will pop out of the box. You can push the part of the balloon that sticks out in, but it will just pop out somewhere else. The trick to this is getting the balloon to stick out somewhere where it bothers you the least. but just understand that unless the entire system, the balloon and the box together, are re-designed, you're going to have something that is not optimal everywhere.
There is a reason the the buffer and the gas key are shorter, and it is an out growth of the revised cam track. If you make the cam track longer the distance the bolt protrudes from the carrier when unlocked is longer by the same amount. For example, the standard AR bolt face is 0.778" from the face of the bolt carrier, if you make the cam track longer by 0.150" the bolt face will now stick out 0.928". The face of the bolt has to move rearward at least 2.8" to get behind the bolt catch, and probably another 0.200" to ensure the catch has time to rise to engage. This means the bolt carrier minimum travel has increased an additional 0.150" to get the face of the bolt back to where it needs to be... It might be more than that if the longer protrusion of the bolt requires repositioning the cam track to keep sufficient 'wheelbase' on the bolt support rings.
As to the Lewis, FG-42, and M60 and why they have such long free travel. Well, first off, they don't have much free travel at all, maybe a 1/10 of and inch maximum. The cam helix is just very shallow over the first half of the run, the illusion is multiplied by the very long actuator stud on the operating rod, making the entire cam look long. But, that aside, remember when we said the longer the free run, the higher the carrier velocity? A higher carrier velocity, means the carrier has more momentum. If the bolt assembly mass is large compared to the carrier/op-rod mass, more velocity will be lost when the carrier/op-rod has to pick up that mass and bring it rearward. The mass of the Lewis, FG-42 and M60 bolt assembly is fairly substantial compared to the op-rod mass, and the Lewis and M60 need a lot of energy (velocity) to run the feed systems. Also, these weapons have helical locking surfaces, which means as the bolt unlock the bolt also moves rearward slightly, initiating slow extraction during unlocking, the very shallow cam helix is done to maximize the mechanical advantage of the actuator stud in the cam track.
And, yes.
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