To add, the best way for economy, read the lights, read the traffic, read the road, judge your gears to the situation you are in, easy breaking, smooth acceleration, use the right gears up hills ( Not an Issue with an Auto) make sure your car is serviced correct, tyres correct pressures, windows up, this all accounts to the usage of extra fuel, unnecessary weight in the car, filling the car to the Brim when you only doing short trips.
Nowadays, it normally isn't. Apart from the control aspect mentioned by TWR, in most modern vehicles (including my truck) if you are coasting in gear, the fuel management system will shut off the fuel (ie you are not using any). If you coast out of gear, the engine has still got to run, so will use a bit of fuel. OK, it might not be a lot, but you wouldn't save enough to make it worthwhile...unless you were freewheeling off the top of Ben Nevis or something!!
Of course it does make stalling as you slow down, less likely. I tend to think the outrage at doing this is over the top. Unconvinced a situation will emerge that needs you to already be in gear than slam it into gear, given the slowing down intent anyway.
The brakes will work with the IGN key in the on position O.G. but the steering will lock up if the key is switch to the off position & the brakes will become very hard to press as there is no vacuum getting produced. still a dangerous thing to do.
The car's in neutral, coasting with the engine running. The steering lock doesn't engage till the key is removed and there are many, many worse thing you can do with a car than coast to a halt.
Not saying it is right or wrong to coast in neutral ... when your car engine is running at tick over and coasting with no load ( gear engaged). Then it is at it's most efficient.