Regarding Brussels Airport:
Brussels Airport has 1 terminal with 2 concourses A & B.
The A concourse is reserved for schengen-flights only => no immigration.
There is a central security screening before the shops at the end of the tunnel which leads from the terminal under the taxiway to the concourse.
Passengers departing and arriving from this concourse mix, there is only one level (gate area).
The B concourse is reserved for non-schengen flights only => immigration.
There is a central security screening after the shops at the beginning of the concourse and one in the middle of the concourse for transit passengers.
Passengers arriving from a flight are separated from departing passengers as they arrive on different levels. Arriving passengers in this concourse always have to pass a security screening before they are allowed in the departing area. They have however access to the shops as these are before security screening and these shops are located in the international transfer area (before clearing immigration).
In addition there are also T-gates used for Africa flights of brussels airlines . They are located at the end of the A-concourse with an exit immigration check. As the A-concourse doesn't has a separate level for arriving passengers this part of the concourse is only used for departing passengers and arriving passengers are transferred to the B concourse were they can clear immigration.
So to me the separation of arriving and departing passengers is used to have a uniform security screening as all the members of the schengen area (probably also the EU countries) have agreed on the same security screening standards making a additional screening unnecessary for these passengers.
In the USA this apply also. If you once passed a TSA security screening you won't have additional security screening, arriving passengers mix with departing passengers. Flights that has a non TSA security screening ( out USA) will separate arriving passengers and will rescreen passengers that have a connecting flight.
Apparently in AMS arriving passengers mix with departing passengers as the security screening is at the gate. So their is no need to separate them.
From the LH website about overhauling pier B : "the implementation of an EU regulation which stipulates that inbound passengers from countries outside the European Union must be separated from outbound passengers."
Lufthansa - Lufthansa at Frankfurt Airport
This seems to me that the EU wants to free passengers from EU inbound flight not to have an additional screening for connection flight.
Unless there is a mistake in that LH statement: