If you're secret-sharing a symmetric key then you're dealing with computational security anyway, but you do get some notion of integrity for free. As you said,

If you're secret-sharing a symmetric key then you're dealing with computational security anyway, but you do get some notion of integrity for free. As you said, given a reconstructing set of shares you can tell whether all shares are correct, or whether they aren't (but you are not able to identify the bad share). However, if you have additional good shares (enough good shares to reconstruct), then you will be able to identify the bad shares. You could also use digital signatures on the shares to get integrity for individual shares.