My two cents worth
Most ANSPs provide guidelines for controllers based on human factors research. So never should anything requiring a readback be given with a frequency change. Just makes sense really, '..climb FL130 contact centre on120.8...' that would be dumb.
Trouble is the kids (anyone under 35 is a kid to me!!) in this game are no longer exposed to the crews like we were previously. So they just pass on the information they need to without having a little think first, or any consideration for the phase of flight, type of weather being experienced etc etc.
I would much rather make with 3 transmissions with 3 correct readbacks rather than 1 TX with an incorrect and possibly dangerous error contained within it.
Ongoing and refresher training would address this problem, alas most ANSPs fail to provide controllers with any refresher training because of the cost. But that is another thread entirely.