Art Alphin (A-Square) uses the P-14 Enfield and 1917 Enfield actions for his large caliber express rifles. These are mauser style actions with front locking lugs and large diameter bolt. It is also a very long action and is capable of feeding the largest conventional cartridges. Alphin has used them as the platform for .475 A-Squares, various big .500 calibers as well as the awesome .577 Tyranosaur.
The No 5 carbine mentioned uses a weaker, rear-lugged Lee Enfield action, a variant of the actions used on No 4 MkI/MkII and No1 Mk III rifles. You will occasionally see Lee-Enfield sporters in calibers which are wildcats of the .303 British, usually of British, Australian, or Canadian origin. New production Enfields would be expensive to manufacture and less capable than their Mauser style counterparts.
It is true that the Lee-Enfield action is weaker and a bit more complex than Mauser 98 rifles, it is also very smooth and fast, has a large magazine capacity (for a bolt rifle), is easy to clean under battle-field conditions. The No 4 rifles are superior to Mauser rifles in one respect, that being the ease of correcting head spacing. Bolt heads of different sizes can be fitted to correct head space. Mauser rifles would require rebarreling, chamber work, or a barrel set back to correct headspace problems.
No 4 Enfields have been converted to 7.62NATO (not to be confused with .308) sucessfully, so they are fairly capable. When Gibbs first hinted at the .45-70 Enfields, some posters did calculations to estimate the acceptable chamber pressure for the .45-70. The action should be safe with all Winchester, Federal, etc loads, and has the ability to go a bit higher. The safety factor was only marginal when it comes the 40K PSI Buffalo Bore-type loads, where the bolt thrust may cause locking lug set back with repeated firings.