Cross bolts are almost as old as bolt action rifles, and as Brit said above are there to reinforce and stop the stock from splitting, especially on big heavy recoiling calibres. Properly fitted the recoil lug should bear against the cross bolt. I have a copy of Clyde Bakers "modern gunsmithing" written in the 1930s. He was of the view that cross bolts are needed on machine made stocks as the in letting has to remove quite a bit of wood around the action, but that unless fitted properly, don't actually do very much. On a properly hand inlet stock you leave a lot more wood in and around the action thus making it a lot more secure. The biggest cause of stock splitting is any movement between action and stock. Try pressing a nail into a piece of wood - very difficult, but easy to tap it in with a light hammer.
Grain of the wood is also important and it should have nice straight grain through the action and grip. Hand in letting stocks takes a lot of time and patience which just adds to cost. Nowadays with modern machine tools, in letting can be very much more precise - most of the Italian made shotgun stocks including side locks are now made on CNC mills, leaving plenty of wood in place. Glass bedding with modern epoxies also does the same job. Epoxies are wonderful materials, but they do break down over time. Probably not an issue for us reading this, but question over how many glass bedded rifles will still be is use in 100 years time?