It is clear it is not a good idea to do resampling in a particle filter if the robot is not moving (there is no action), as the particles will converge towards a simple particle.
However, Probabilistic Robotics book quickly mentions "It is usually a good idea to stop measurement integration if the robot does not move". However, I am not able to fully understand why.
My only guess is that, if robot does not move the sampling (which not resampling) will give the same particles. Therefore, is there any other negative effect other than wasting computational power? Because in a world with lots of noise I think it might be helpful to keep the sampling running to have move proper weights over time.