so how about turning this discussion around, now we are saying why a movement should choose a non-violent path over a violent one.
So what about saying how a governement could make a violent movement turn into a non-violent one.

Off course a first possibility is to force them to become non-violent by using enough force to compell them abandon violence, but violence alone might not be the most effective way to do this in some cases.

A second option might be to make use of less force, and make use of other options than the military one.
So a first step by the government side is determine which of the enemies political goals can be negotiated about and which cant, and also determining what grievances excist that cause the movement to be popular in the first place.
(in afghanistan something that cant be negotiated about might be the implementation of sharia law, but certain other demands, demands that are more important to the rank and file taliban can be adressed, im thinking about things like poverty or corruption here)

A second step might be then to encourage/create non-violent protest and adopting a policy to negotiate only with the non-violent movements and not with the violent ones, and important thing here might be to grant the non-violent movement some consessions to show that a non-violent aproach actually works. What can also be considered is actually creating protests instead of waiting for them to actually happen, a bit like agent provocateurs but then in reverse.

Another important issue is the use of force in this strategy, force might be used to isolate and demoralize a violent movement and combined with an amnesty program, maybe using converted militants to denounce violence and dicredit the violent movement and praise the non-violent one.

Off course during the creation of the actual non-violent movement the government should be carefull about separating the more moderate and acceptable ideas (which should be encouraged) and the more radical and unacceptable ideas (which should be discouraged and marginalized as much as possible).

Important to note is that the now non-violent militants are not working for the government in an attempt to gain better governance but they are still working more or less against the government and thus could potentially count on more support and they could avoid getting the label of "traitor".
Off course it is still important to prevent the non-violent movement from leaning too much towards the violent one so a bit of covert guiding by the government might be usefull.

Also important is the fact that such an aproach should be adapted to the culture, political structure, social and economical situation..etc off a certain country/area.