Networked parasails working in yo-yo mode could look like Daisy’s network, the parasails replacing the lifter kites, and also being used without the rotary devices.
The argument in favor of networks could apply in this specific case, to avoid this (for unnetworked AWES):
Trains of parasails could perhaps increase the total swept area.
It is not impossible at first glance to imagine that some parasails or parasail trains are in the power reel-out phase while others are in the depower reel-in phase within the same network, leading to continuous power.
That said, to supply continuous power, several (2 or 3 at a minimum and not much more at a maximum) networks of parasails with offsets may be better suited to provide the reel-out and reel-in phases in the same time. But in that case, a least one parasail for each network, always in action, would be necessary to ensure a minimum of lift during the depower reel-in phases.
There would be several ground stations, but less than for unnetworked parasails.