Now doubt, headers and sidepipes on Sharks are good looking and recall that "road racing" look of 40 years ago.

They also, obviously, make a huge change in how the car sounds, both inside and outside. Lastly, performance with headers and sidepipes will improve over stock exhaust.
Downsides?:confused
There are several. First, virtually all header/sidepipe assemblies have primary pipe lengths that are usually too long for the best exhaust tuning. Secondly, it's very difficult to have an exhaust crossover and impossible to have an X-pipe, two additions that most modern, high-performance exhaust systems have. Lastly, unless you are going to drive with open exhaust (which, other than on a race track or if your already deaf, you won't do for long), there's usually a significant performance loss when you add the "slip-in" mufflers that go into the sidepipes.
A good set of under-chassis headers and a well designed and installed 2.5 or 3.0-in exhaust system will usually out-perform headers and side pipes. In fact, a good under-chassis header and exhaust system with proper low-restriction mufflers may outperfom open-exhaust sidepipes.
On the stainless steel vs. ceramic-metallic coated mild steel issue...obviously, the best way to go is stainless but it's freakin' expensive. For stainless headers and sidepipes, I betcha you'd be talking 2500 bucks just for the parts.
Weigh those pluses and minuses.
It was said earlier that there is doubt about ceramic metallic coatings thermally insulating exhaust systems. WTF? That's rediculous.

Not only is there no doubt, but there is plenty of evidence that cerametallic coatings reduce heat radiation from exhaust systems. Because "Xplosive Performance" is in the Corvette parts and service business, a certain level of knowledge is assumed by customers. It seems to me, since exhaust systems are a big seller, part of that knowledge customers expect is an understanding of exhaust system coatings and their benefits. I suggest that if there's doubt, some basic research into coatings will remove that doubt or...test the idea yourself, using the resources you have available at your shop.
As for the corrosion issue, it is true that exhaust systems are more liable to corrode from inside out, but 1) there are some coaters who can coat the inside of exhaust systems and 2) most street high-performance, aftermarket systems which are aluminized mild steel tubing and then are coated are going to last a long, long time. The only exception would be systems on cars which are driven in cold winter weather in areas w on roads which are salted. If you drive your Vette in snow and ice and on salted roads, go with a stainless system.