To the OP, the barreled action is the race car's engine. Everything else, including the stock/chassis, is the ergonomic interface by which you drive the car. Find what works best for you in terms of fit and features. I personally own a Manners T4A and an AI AX. Love them both. Both have some similarities but some obvious differences. I like the way the AX fits me. I like the pistol grip. The side folding butt is rock solid in the folded position. Some other chassis systems have weak or no detent in the folded position. I sometime run the AX with forward mounted NV so the modular attachment points on the forend are a good feature for my uses. The chassis also has good balance for my rifle. Love my AX chassis and I wouldn't change anything about the rifle.
That is not our experience with some chassis systems. The AICS, AI AX and a few others are generally good to go without needing skim bedding. My personal experience with the McRee is also that it should be good to go. But there are a few other chassis systems that tend to perform a lot better with skim bedding.
Mark