The acoustic performance depends on the resonant pitches of the parts of the guitar, and how they work together. The 'wood' resonant pitches depend on the relationship between the stiffness and density of the wood. Wood is stiffest when the fibers run parallel to the surface, so cutting through the wood at an angle reduces the stiffness a bit at a given thickness, or requires a bit of extra material to get the stiffness back up to where you want it. Either way the sound is changed. I'll note that it takes a pretty large angle to make much difference in the stiffness of a top, though. We usually worry about run out in flat tops long before that point.
Arch top instruments have, of course, been made using tops that were bent to shape. Most recently we see this in 'affordable' factory produced archtop guitars and basses, but back in the day it was more common on some types of high-end instruments. Viols da gamba tended to use multi-piece tops where the central pieces were bent to rough shape and finish carved. A lot of such construction methods make sense if you take the mind set that wood was expensive and hard to get, while labor was relatively cheap.
Modern bent tops tend to be laminated, with cross plies. That more less automatically limits the performance IMO, due to built-in stresses and glue lines, if nothing else. There has been discussion in the violin world on and off for a long time about non-laminated bent wood tops. Advocates feel they should work better, but so far as I can tell no major benefits have been demonstrated. At one point some folks looked closely at some Stradivari instruments, and found no evidence that they were made of bent wood, so the notion has been pretty well dismissed in that corner of the lutherie universe.
