My last job in Fort Worth, the guy wanted his driveway to look like an old country lane, not a new pour. I ended up using a stiff brush and just dabbing it randomly to break up that smooth look. Honestly, some clients have a picture in their head that has nothing to do with textbook perfect. Tbh your wet broom trick is basically the professional version of what I had to figure out on the spot. It's smart because it adds grip without making it look messy.
A wet broom for the second pass is actually a pretty smart fix. I've never heard a client complain about a finish being TOO good before, that's a new one. Gotta love Dallas homeowners and their very specific patio texture needs.