. . . I'm rather impressed just how well the "flexy" Remington action managed to stand up to the stiffer body Custom actions with their longer and larger thread tennons and their smooth operation.
I do wonder how many of those were barrel blocked.
But you have a point. Both Joel Pendergraft & Charles Bailey use 700s on their big tube guns -- these are HGs, not LGs. The only thing the action does is to serve as a breech block, & neither of them felt the expense of a custom action was required. Both do their own work; any action truing costs only time.
As to speed: if, like some of us, you grew up with a right bolt, right port, you can shoot that pretty fast, particularly with a big 1K chamberings. Open the bolt with the right hand, pull it back with the left while loading with the right hand. Run the bolt forward with the left hand, close it with the right as the left drops to either the bag (LG) or rear pedestal (HG); you're a bit faster acquiring the target this way. Because Joel's HG "stock" got in the way of pulling the bolt back with his left hand, we added a short rod, pointing straight out, to the bolt shroud on the left side so he could pull the bolt back with his left hand. I don't think anyone shoots 10 shots faster than Joel.
Come to think on it, I'm currently shooting a RBRP (drop port) Viper in point-blank BR. No coned barrel with a drop port. So how is this any faster than a Remington?
Edit: Aside from barrel blocking, some of the Remingtons used at Hawks Ridge are sleeved -- big sleeves, too, some of them steel in HG.
And as far as pulling the bolt back with your left hand, I have an early BAT 10-inch action (single digit serial number), where Bruce only allowed .001 clearance with the bolt. With the tight fit, long bolt throw, & long handle, it will bind. Faster to grab the handle at the root with the left hand & pull it back once you've opened it.
Below a picture of Joel's HG using a Remington 700.