1000V/m is a huge field for the conductor we are considering!
What do you think is providing a counter force of 10,000 N per atom so that there’s no net acceleration? What is the total pressure exerted by this counter force?
edit: 10,000 N in total. Not per atom
I do this experiment each time I connect a mercury switch in a circuit. If the liquid was moving, it and the current would soon start to oscillate.