Do people actually lose large amounts of money due to ID theft? I've always considered ID theft to be the lenders being defrauded, and while it is a huge hassle to get sorted, the real person isn't legally liable for the debt fraudulently obtained in his name.
Also, if you think money is a bad idea, what else do you propose? I'd rather take money with the chance of losing it rather than no money and "credit monitoring" which doesn't actually prevent ID theft, only alerts you after it's already too late.
If anything, the money idea actually makes sense as insurance for future losses due to potential ID theft.
Surely it's typical for credit unions to have deposit insurance? If not, there should be regulations in place to ensure people understand that they are basically just shareholders.