Perhaps a better time to notify the crew of your expectations would be prior to getting them airborne, when you need immediate compliance and response. If this is a frequent expectation of ATC, put it on ATIS like LAHSO, so they can let you know if they'll be unable.

Diplomatic refusal or not, ATC gave them the option of saying no and painted themselves into a corner when that's the answer they got.

I'm all for exercising options that allow us to expedite departures when it makes sense. There are pilots out there who refuse to accept visual approaches by "following traffic" because they don't want the shift in responsibility re: wake turb & separation off ATC and on to them. They'll probably be the minority that will stiff you on this kind of departure request. Therefore, you need to make plans for dealing with the 1% factor.