My understanding is that one of the roles the side-firing tweeter plays, and maybe even the primary role it plays, is correcting the spectral balance of the in-room reflection field. (I'm sure it has some effect on spatial quality as well.)
The flat electrostatic panels will beam, resulting in significantly less high-frequency energy in the reflection field than in the direct sound. To correct or at least reduce the spectral discrepancy between the two, the side-firing tweeter's power response is tipped up, such that it "zigs" where the panel's off-axis response "zags".
I used to do something similar when I was running Quad 57s. Ime it works and works well. Whether or not it would "measure" well, I don't know.
Here is the actual reason given on their website
“The airLayer comprises high grade, silk dome (Carmelita) or silk ring-dome (Valentina) tweeters mounted to the outboard side of each speaker. Their sound strikes and reflects from each speaker's near side wall and diffuses about the room.This was initially an option, but everyone ordered the speakers with it, so it was made standard.
Their levels can be adjusted from silent to overly loud by turning a dial on the back of the speaker. This adjustability lets you get the right effect in any room, regardless of wall distance, room reverberancy, or symmetry.
What effect is that? It actually produces two different effects at once, and serves two purposes: providing an extra layer of 'air' when seated, and treble compensation when up and walking around.”
I can tell you first hand that in person David Janszen said they were there for people who enjoy the added sense of spaciousness they provide.