I totally can understand the need to hold the ID, but what about the CC? Do you think it's ok that they take your CC out of your possession? Half a year ago I handed my Debit card to the front desk of an IHG hotel and she took it to the back and 6 weeks later someone emptied my bank account (that was the only time the card was not in my possession).
During my last trip I stayed at a La Quinta, the front desk also demanded to take my card away and they basically treat everyone as con artist. I asked what if I only have a digital card and she said then I can't check in. It's crazy.