Engine wind down
 

Can someone briefly explain why I see some people shift into neutral after a drag run? I think it has something to do with not damaging the engine while slowing down????

Those people just like to wear down their brakes. Engine braking allows cool air to cycle through the engine cooling it down, while at the same time saving their brakes somewhat.

People, in general, seem to think it's cool to coast in neutral.

I am vehemently against being in neutral at any time while the vehicle is in motion.

After a drag run, I coast in gear for a few seconds before beginning to actively brake/downshift to slow down. You can't always coast that far before you run out of road (even if you always go down to the NHRA turn off every time), so I dunno how much brake you really save, either way. It's a nice cool down tho, keep the water and oil pumps spun up without any actual load being on the engine, or any fuel really being burned will get the temps down a lot faster, especially with air still being forced through the radiators and whatnot.