One advantage to sitting down and talking with judges afterward is that you can get very explicit qualitative feedback and you can ask follow-up questions.
One disadvantage is that it's very time consuming and labor intensive for the judges. Can you imagine if they had to give a five-minute critique to every skater in every event? That would take longer than the events themselves, especially if multiple judges critique each skater. So that kind of feedback is rare, has to be solicited specifically, and sometimes involves extra expense (higher entry fees for competitions that offer critiques; traveling to skate for and meet with a specific judge for individual critique or more likely paying for the judge to travel to where the skater is). In most competitions there's no mechanism set up to get detailed direct feedback from judges because there just isn't enough time.
Also, judges aren't allowed to talk to skater A about how they judged skater B. So those kinds of critiques don't give any comparative information the way actual scores do.
Protocols will show where skater B earned more points. If skater A looks at the protocols and looks at the videos and sees that the judges scored B higher on this element or that component, she may be able to see for herself how B was better. In many cases under IJS, the answer is in the base marks for the calls made by the technical panel, not the judges. E.g., if B gets credit for two double axels and A gets downgrades on both her attempts, that might be the answer right there.
If the areas where B was better are not apparent to A and her coach even after studying the protocols and videos, there's no official mechanism under any judging system to tell her "B skated faster and jumped higher and spun faster and had a better balance of clockwise and counterclockwise skating, so those areas trumped the areas were A was better." If A is unable to see the difference in speed and jump height if that was the deciding factor, for example, or is unable to see the difference in jump rotation if that was the difference, then she will remain bewildered either way.
The protocols just show the numbers, not the thought processes -- if a skater really wants to know what a judge was thinking, she still needs to find the judge and ask. And with anonymous judging in international events, it isn't possible to identify which judges gave which marks so you wouldn't know who to ask about what.