It's kind of odd that people are so against this - I got stuck with no cash and a *very* low fuel tank the other week and needed to get to work and home (15kms each way) on as little fuel as possible, so I used the same rationale as the OP -
Accelerate up to speed, identify where your next intersection is and take a guess at how much momentum you need to get you there by coasting. Instead of braking late, you start slowing down early instead, if you gauge it just right, no braking is required at the intersection. I drive a manual, so when I need to get back into gear, pick one to suit, rev match, click it in and off you go smooth as.
It got me thinking about how much fuel it actually saves, so I did a very rudimentary unscientific economy test, and managed about 320kms from my tanks halfway point deliberately trying to optimise time spent in neutral, where I usually get 250kms with normal driving (all values are approximates).
With regards to the safety aspect, if you are going to drive unsafely you shouldn't be on the road. Is this an unsafe practice? It depends - I drive country roads to work with little to no traffic, and the terrain is extremely flat, so I don't have to contend with hills. If there is other traffic around, I will change my habit to a more traditional style of driving, but so long as there's noone around, me coasting slowly to intersections is hardly unsafe.
PS I can't advocate switching off the engine while coasting, particularly on newer cars where I find you lose power steering, and some braking ability