Yawing causes sideslip
Are you sure of that ? Most analyses would have it that, once the initial problem is under control (considered to occur instinctively for the trained pilot) and the aircraft is flying straight, it is the pilot rudder input causing the sideslip .. hence the need for some bank to reduce the sideslip in near Vmc situations.
Pilot is required to give rudder input to stop the sideslip.
Perhaps the rudder input is to control the asymmetric thrust yawing moment ? At low speed, where the concern is greatest, the relevant pilot input is to bank into the operating engine(s) to reduce sideslip... noting that some systems have a problem with small angles of bank so the sideslip has to be accommodated due to other considerations.
Giving rudder input for zero sideslip will require too much rudder deflection.
Perhaps you can explain just how rudder input can result in zero sideslip ? .. presuming wings level.
Airbus found a 'sideslip compromise' which overall reduces the drag by limiting rudder deflection.
I have no specific knowledge of how the indicator functions. However, I suggest that the idea is to reduce sideslip to a value somewhere near zero.
On acceleration, this problem ends, hence when flaps are retracted normal sideslip indicator resumes.
Or, perhaps, sideslip related drag is critical at low speed but, to a large extent, can be ignored at higher speed to reduce pilot manipulative workload ?
A question, though, from a non-AB pilot - do you conduct the initial climb out wings level or with some bank into the operating engine(s) ?