shouldn't a heading, if you're on one, be part of the initial call on a handover anyway (standard phraseology)? Thereby negating the need to instruct us to say so.
Reduction of workload by self-organising is a major contributing succes and survival factor for an ATCO. A silent handover is one of the workload-reducing techniques.
Silent handovers are made possible by automatically derived electronic messages, even between different ATC units. In advanced systems the headings originated and fixed by the radar controller (mostly called radar heading but that is the subject of another thread) can be included in system to system messages. That's ideal but rarely applied in operational systems yet.
In less advanced systems there are two options, either a telephone coordination (as advocated by Chesty M) leaving the pilot out of the game but consuming precious ATC time. It may not be your own ATC time, but also the ATC time at the other side of the boundary which you are unaware of at your side. A good controller takes account of this, it may be very embarassing if one is called in the middle of peak traffic to answer a superfluous coordination message.
The other option is asking the pilot to report the a/c heading on the next freq which is I'd think a minor workload detail for a pilot, certainlly at cruise altitude.
Not everyone reports their heading even when told to do so.
If the radar instructed heading is to achieve a critical separation of barely 5 miles it is even wise to apply both techniques, the coordination message + the assurance through the pilot's message. If, at the other extreme, the radar heading is far away from other traffic allowing a further shortcut in the adjacent sector courtesy next controller, the instruction to the pilot to include his or her radar heading in the initial call is a very clever way of reducing one's own workload.