"This law is just too black and white."
That's the complete opposite of the usual complaint, which is that it is too grey and unclear.
It's entirely down to the headteacher's discretion, as far as the law is concerned.
The LEA has no role in authorising leave.
If you have a good HT, then the individual circumstances can (and are) considered and holidays can be authorised.
I don't think setting a new policy, which would mean families who are lucky enough that all their children have been healthy that year can have a holiday but those whose attendance is lower would still get fined, is remotely acceptable and would hope it is immediately challenged under DDA.
If you want things like overall attendance, health circumstances and other individual circumstances to be taken into account by a nominated member of staff in the specific school who if authorised by law to use their common sense, the you get the law as it actually is at the moment.