I agree there is no reason for you to offer a reduction, there is no reduction in cost to you, you still have to prepare the home no matter what time they arrive.
Also unless this is a whole house listing with electronic check in, I would restrict the check in time say until 11 p.m. You don't want to be waiting up all hours for guests to arrive.
Also your prices are ridiculously cheap already, I can't believe the cheek of your guest to ask for a discount.
Have you compared prices locally for comparable properties?
You might want to increase your prices if the market shows you are undercharging?