How about reading back assigned speeds and headings on a new freq?

Ex, assigned heading 280 after takeoff by tower, do you tell departure you're on a 280 heading?

Or center gives you 320 knots or greater, do you need to inform the next center controller?

I was taught that they already know what you're assigned, and not to repeat it unless the controller asks you to. But I just flew with a captain who's convinced you always repeat heading and speed regardless. Can we get a consensus on this?