The Balanced Field principal is a technique used by Performance Engineers in producing data which has some advantages in simplification, and, for a degree of performance optimisation. As you've stated, for the BFL, TODR = ASDR, and Stopway and/or Clearway are generally not considered. If Stopway and Clearway are to be considered, then they must be equal to each other for the BFL principal to remain. In this latter case, the requirement for a minimum percentage of the airborne portion of the continued OEI Takeoff to the screen height must be considered by the Performance Engineer to be above the TORA, and will be obvious to the "end user" pilot as a limitation upon how much credit may be taken for Stopway and/or Clearway.
There are no mystical / religious attributes to the BFL principal, it is a convenient system for certification purposes. My own preference is to work with Unbalanced Field Data.
The Unbalanced Field is one where the TODR is not equal to the ASDR, it's as simple as that. Accelerate-Stop and Continued Takeoff performance must be calculated separately, and the Takeoff limited to the lesser of the 2 limits arising.
Consider this example. The TORA is 2000 M, but, due to obstacles, the Effective Operational Length of the field becomes 1700 M (You must have reached screen height by 1700 M to optimise Takeoff Distance requirements against a shallower gradient to the critical obstacle). If you're using BFL data, the Accelerate-Stop must also be contained within 1700 M, even though 2000 M remains available. This is probably not a great problem in day to day operations, but now throw in Anti-Skid Inoperative (which only affects Accelerate-Stop and has no effect upon the continued Takeoff), and the significantly affected Accelerate-Stop performance is further artificially worsened by limiting ASDA to 1700 M whereas 2000 M was available.
To address your last question, Yes, all performance must be Mass / Weight limited to comply with the TODA,TORA, and ASDA.
That's the thumbnail sketch, it can be developed much further.
Regards,
Old Smokey