I've never been on an admissions committee for anything so I don't know what I'm talking about. But I'm guessing ECs and LoRs are more useful to admissions committees as red flags than game-changers. I assume that the vast majority of candidates have glowing letters of reference, since we can hand-pick the professors most likely to write amazing letters. But if a candidate has a mediocre letter of reference despite their being able to choose their referee, it's probably a red flag. Same with ECs: most candidates were probably very involved during undergrad, so there probably isn't much that would make someone stand out from the crowd on that front. But a candidate with no ECs with no explanation for why would be a red flag.
Also, a while back I was doing some admin work for a grad program at my university and ended up talking to some of the admissions committee members. This was a public policy program, but they told me they gave no weight whatsoever to the position of referees, so long as they fulfilled the positional requirements (e.g. a professor, or a supervisor for mature applicants). They gave the applicant a certain number of points based completely on the content of the reference letter, and combined that score with points from GPA, standardized testing, other softs, etc. Everyone above a certain threshold got in (unless they had significant red flags), everyone below a certain threshold was rejected (unless they had some amazing game-changer), and everyone on the bubble was put through a second round and discussed in committee. No idea how other places do it, or even if any law schools do anything remotely like this. But I doubt it matters if the letter of reference is from someone in a position of major influence or not