Slack is almost always bad when you are belaying someone below you, especially on steep angles when , whether your anchor is stationary (a picket) or moving (a climber). Almost right, f=m*a (mass x acceleration) equals force. The longer you fall, the higher the acceleration. The higher the acceleration, the higher the force. momentum equals mass * velocity (p=m*v) . Simple physics.
However, a dynamic belay is better than a static belay. Letting rope slip, as in a boot-axe or body belay, distributes the force (or the impulse) over a longer period of time. therefore, the anchor sees a lower maximum force. impulse (Ft)=mass* final velocity - mass * initial velocity. Impulse is the change in the momentum of a body (or falling climber) caused over a very short time. J = F delta t = delta p . delta means change in.
Just trying to break down the arguments into their component parts using physics.
Of course there are a few more variables to consider. Like is the belayer's self arrest able to withstand a greater force than a boot axe belay? Likely not. considering he is also trying to stop the forces his body is generating if he is moving. So maybe a little bit of slack is good to allow ... I dont have time to go into it. so if some engineer or physicist would like to take up the gauntlet, please educate!
Thanks Issac Newton!