The ones I mow on Thursday will be ones that won't care. I only take care of a handful that would have something going on anyway.
If you are in this business, taking a day of in the middle of summer isn't always possible. Why throw off a schedule if you don't have to? Seven days of growth with all this rain is bad enough. The Thursday people might understand why it got done off schedule, but suppose you have a washout on Friday. You are trying to catch some of the Thursday lawns on Saturday, and some Friday lawns might not get cut until Monday. And so on.
I don't need a day off bad enough to worry about it. If you can get all your stuff done by to tomorrow and be ahead, go for it. But you are going to have some 8-day growth next week.