Inconvenient as it may be, the reporting of heading or speed is in fact the only guarantee the next controller has of your separation against other traffic. That, most of the time, is why the restriction is given. In order to reduce time spent coordinating, it says in the MATS for LATCC (and most units I believe) that the next controller must be informed if the aircraft is on a heading, either by telephone or by asking the pilot to report the fact. So by not doing so you increase R/T and your own loading because we have to check.
Don't get me wrong, I do appreciate that you are not always sitting up there with your feet on the coaming, but these are important instructions which guarantee your separation so they should have your attention. They are not done for the fun of it.
Also agree with the multiple instruction transmission problem, but would point out that most controllers will/should not give level instructions at the same time as a frequency change.
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"Take-off is optional, Landing is mandatory"