... one does not choose the V1 so the ASD to meet the ASDA. V1 is selected so ASD=TOD and that's what balanced take off is all about.
To state that balanced take means that ASDA=TODA is the same as to state that IF a takeoff is balanced then you are limited by the runway lenght and that's not true at all.
This is clearly indicated on any RTOW chart.
On the first point - you
would choose V1 to get ASD(R)=ASDA if you were trying to get out of an airfield where you were being limited by the "stop" case, either due to a disparity in "go" and "stop" performance or a disparity in ASDA and TODA. V1 is selected to make ASD(R)=TOD(R) if you wish to have a BFL(R) - but that's unlikely to be the optimal case for a given airfield unless it happens to have a BFL(A).
In fact, a BFLR aircraft is more likely to be restricted by the runway than a non BFLR aircraft unless the field itself is balanced i.e. BFLA. So the two concepts do have a linkage.
BFL(R) is a simplification for ease of use, just as much as BFL(A) is. In both cases you are giving up some flexibility in scheduling speeds (and hence losing efficiency of operations) in order to obtain simplification.