I have a potentially more optimistic (and simultaneously more pessimistic!) view to offer.

Some differing interpretations of the law distinguish between the lawmakers' intention vs the literal meaning (and keep in mind that language itself changes a lot in just a few centuries. The hard problem is that, in PL terms, the law is written in syntax without agreed upon semantics. So a decent step could be just using some agreed upon semantics, like we do in code! Then at least "interpreting" it would be unambiguous.

Maybe a decent analogy would be gcc vs clang might produce different programs for certain undefined behavior, and different combinations of pieces might lead to different behavior too (like race conditions), and somebody (the plaintiff/user) is asking you (the judge/compiler) to decide what's going to happen in this next loop/program/whatever.

Or maybe a decent analogy would be getting a ticket that the API is erroring in some rare user's case and having to look into the code and stacktrace to realize it's some weird unanticipated interaction between two different pieces of legacy code (150 year old law) that now interact due to a recent merge (a new law from last year), and now it's crashing, so we have to figure out how to interpret/compile/resolve this user's case.

If law was usable like code, we'd never have any of those issues, just like we never have those issues with actual literal programs. And when we do, it's just because we're using the wrong language/aren't encoding enough things in the types and semantics/shouldn't have used this niche compiler so now let's get a new interpretation from another Supreme Compiler/etc. Life would be easier \s

So it's maybe more optimistic than you, in that the run/read time power (judicial) doesn't get diminished, but more pessimistic in that I believe it because I believe that changing the language from english law jargon to some formal language doesn't actually eliminate the issues it might be intended to eliminate.