This is likely the reason. In all the hotels in which I worked, it was cheaper to process a credit card that was present (aka swiped through the machine) than one not present. If I remember correctly from when I worked in an hotel accounting position, I think the difference in pricing was contingent upon the number of chargebacks relating to those non-present cards (aka stolen cards).

All of the hotels I worked were business hotels with a ton of repeat guests and the bulk of our "new" guests were usually related to existing local corporate accounts. Stolen cards were not a significant issue. As a result, the policy was to use the card on file (meaning it didn't have to be swiped) if the guest requested.

A Hampton Inn along an interstate would have a very different clientele. Those properties would have far fewer repeat guests and not many local corporate accounts. Those factors mean they are far more prone to processing stolen cards. As such, I understand the reasoning as to why a hotel would require a card to be present.