Two reasons come to mind, to get that look and to retain heat energy in the exhaust manifold.

Straight up we need to know that Ceramic coating is the best option for a permanent clean look. Exhaust wrap will not stay looking pretty forever.  The wrap will come loose over time and need to be re-tensioned. Wrap is susceptible to fluids causing degradation and ageing. More on this later.
The more common reason comes back to heat. Keeping heat out of the engine bay and keeping heat energy in the exhaust manifold. Keeping the heat out of the engine bay will aid the life engine bay components and increase the efficiency of the radiators and coolers. Keeping engine bay heat away from plastic parts, HT leads and wiring reducing heat stress and fatigue. Inlet piping staying cooler in turn keeps the incoming air colder and denser.
Keeping this heat in exhaust will maintain a faster exhaust velocity. This is an important factor for coating or wrapping. Hotter exhaust gas moves faster. Faster moving gas will aid the scavenging of cylinders and promote a faster turbo spool. 
It makes basic sense that all of these benefits will add power and torque. I am not taking massive power gains but measurable power gains.
An important point to consider is the thickness of the coating or the Lagging. Many ceramic coatings are applied thin. Coatings are often 30-50 microns. Common terms are cosmetic coating and functional coating. Cosmetic coating is done purely for looks and may not even be coated internally. 
When ceramic coating is applied to the interior of the section, the interior coating aids to prevent the material absorbing heat. With the exterior coating retaining heat in the material. Exhaust wrap on the other hand is only able to be applied to the exterior surface. The exhaust wrap does retain the heat while allowing the manifold to still absorb heat. Heat causes expansion and this is a reason why heat wrapped manifolds may crack due to the increased expansion.

 There are a number of different types of ceramic coating and heat wrap. For ceramic coating the temperature tolerance is from 1050 degrees C for motorsport applications, 650 degrees C for high performance and spirited road use and 425 degrees C for dress up. Generally speaking black has the highest temperature tolerance with chrome being lower and the pretty colours the lowest of the range.
Somewhere it needs to be mentioned that if you have a mild steel manifold it is critical to have a complete coverage of the manifold when ceramic coating is used.  One problem area is the merge. The merge will be the first area of show signs of corrosion when incomplete coverage occurs. 
Wrap is generally made of either, glass fibre or Titanium. Glass fibre is the most cost effective option for temperatures up to 650 degrees C. Interestingly the same temperature as the performance ceramic coating.  As heat protection needs go up to temperatures of 980 degrees C Titanium is the option best suited.
Ceramic coating does have the advantage over wrap from a durability perspective. It will not be damaged by engine fluids unlike wrap which will degrade if in contacts engine oils, degreasers and or other under bonnet fluids.
Turbo blankets fall into a similar category. They work but durability can be an issue
For maximum heat retention you would do both wrap and coat. Yes this does happen.
 
So we know wrap needs to be redone at regular intervals due to lose of tension and fluid contamination where as coating does not. But if the manifold cracks welding with coating is difficult if not impossible.
Wrap does work better at keeping the heat in the manifold. This is undeniable. Remember though the additional will cause more expansion of the manifold and has the potential to cause cracking.
Let’s think about this for a moment, Manufactures use heat shields on exhaust and manifolds. Aftermarket manifolds are most often not supplied with heat shields or proper coating. The reason we go to aftermarket exhaust is to make more power. Extracting more power from your engine will generate more heat. 

Seems silly not to use heat wrap or ceramic coating.