The weaker action will be less ridged which can allow brass to stretch more and provides a less stable platform for good accuracy.
The firing pin hole will likely be larger allowing the primer to extrude into the hole at high pressures, which can lead to primer failure.
Barrel thread tenon may be smaller diameter which can mean the chamber has less resistance to radial stresses, leading to difficult extraction and other expansion issues.
These factors will have little to no effect at standard pressures, but if you want to push pressures with stronger brass, then the increased strength and tolerances of the custom action are desirable traits.
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