Your thought exercise is basically the “local hidden variable” interpretation of QM - somehow, the system already has an internal state when the shoes were sent to Alice and Bob.

Where things get hairy is that if you didn’t know which shoe Alice got AND the handedness of the shoe were genuinely indeterminate (ie, they could truly be either left or right shoe), then measuring one as R or L causes the other to “become” L or R.

The insight is that it’s not that Alice is measuring reality when she sees a left shoe in her box - she is creating reality by seeing a left shoe in her box which causes Bob’s reality to also snap into place at a speed faster than light…and that is the crux of the issue - information should not be travelling FTL.