I presume the point of the checklist is to attempt a start as a matter of urgency, before the residual fan speed decays. If you reduce the thrust lever to idle you may excacerbate the problem. If one or both engines fail to start, the reference items call for the thrust lever(s) to be closed.
Precisely. When in doubt read the manual and all will be revealed. For example try Boeing FCTM Page 8.8 Loss of Thrust on Both Engines, which amplifies the subject.
Dual engine failure is a situation that demands prompt action regardles of altitude or speed. Accomplish recall items and establish the appropriate airspeed to immediately attempt a windmill start. There is a higher probability that a windmill start will succeed if the restart attempt is made as soon as possible (or immediately after recognizing an engine failure)
to take advantage of high RPM
By closing the thrust levers as you would normally do for most engine starts the N1 reduces very quickly which contradicts the Boeing advice of taking the advantage of high N1