You are using an ideal current source set to 1 A. This means that whichever load you attach to it, it will maintain 1A.
By opening and closing the switch, you are just changing the required voltage the ideal current source needs to maintain the 1A. Even when your switch is opened, it has a certain 'Open conductance'. This means that in the open position, the switch still has 1/1e-6 Ohm = 1000 000 Ohm resistance, which means the ideal current source will employ 1000 000 Volts to maintain the 1A current through it.
You are basically simulating huge sparks and fireworks. Yes, Simscape is also able to simulate those. It will not prevent you from doing so.
This is why the current measurement with scope will always read 1A. Try to add a voltage measurement accross the switch and see the large voltage.