Once the Dutch high speed line is eventually opened, times are scheduled as Amsterdam Central - Brussels 1 hr 44. Since the line soes via Schipol, Brussels times from there would be less. The line does indeed go via Rotterdam; I calculate the time from Brussels as 1hr 1. (Source Wikipedia)
This makes for a time London St P - Amsterdam around 3hrs 35.
Eurostar have said that they are investigating adding Amsterdam as a destination. In practice, running on the Dutch High Speed line will require either considerable modifications to the existing trains or purchase of new trains. The latter will have to wait until revised safety rules are agreed, this year or next.
With a 3hr 35 LonStP - Amst. Central time, the train will be competitive but not all-dominating. But quite clearly, this is not going to happen for at least 3-4 years. And a change of trains, with security on the London-bound trains, would detract from the train's attractiveness.
Skipness 1E:
You are right - zero formalities on exit from Eurostar at all points.