Naxian, I think it's important to understand that increases in test curve - lets say upwards of about 1.25lb - are generally about casting further. A 1.25lb tc rod will cope with about 2oz happily, but anything over that - and let's face it modern carping techniques are generally looking at say 3oz leads plus some kind of PVA baiting arrangement - and you're needing a more stepped up rod to cast that comfortably and accurately.
Lots of very big carp got caught on avon-style rods (Richard Walker, Chris Yates etc). In the early days of carp fishing, most of it was done at close range, so the need to cast more than 20 yards wasn't a consideration. However, the advent of bolt rigs - probably more than any other mechanic detail of carp fishing - enabled anglers to fish further and further out, providing their equipment - rod and increasingly larger reels - allowed them to cast the distance.
Ultimately though the issue that I see with what you're intending to do comes down to fish welfare. Let's say you use the rod you've got in mind, you know for a fact that it can deal with all the pressure you can exert on (lets say) 30lb braid. And you wind the reel clutch down tight, because the last thing you want to have happen is for the fish to get in the snags. So now your set up is absolutely nailed on for giving nothing away. To me, what that means is that the very weakest link in the whole set up now is the hook-hold itself. A carp's mouth is relatively soft flesh... something tells me that if you did hook a really big one in those circumstances with the kind of set up I've described - you've got a really good chance of transferring an amount of force to the hook-hold that it just can't deal with. That would worry me at least a little....