What turnip truck did that logic fall from?
OT is gravy? Labor is gravy? Risk is gravy? Reputation is gravy?
Then again, if one doesn't do anything of value during the first four hours, it's reasonable to assume the fifth or sixth will match it.
Those things have to be accounted for for sure, and they are accounted for in the base rate and or rate you contracted the event for right?
My only point/question is: Why are those things suddenly "worth more" per hour simply because the need for them was seen at the event itself instead of being contracted for up-front? Why should that hour cost the client more than a stated hourly rate that was contracted for?
(And let's remember: "Because they will pay 'x'" doesn't constitute a basis for the increased price itself.)
If an answer to that question can't be tied to actual tangibles (i.e. some additional hard-cost incurred on your side or some actual benefit the client receives in that last hour they didn't during the first 4/5), then the turnip truck logic remains unassailed.