For me it would be a matter of personal strategy. Basically, is standing on principle the most strategic thing I can do given my goals in the situation that left me on the receiving end of a polygraph?

Even if my strategic goal is to show that a polygraph is meaningless, being able to pass or fail one at will could be really useful to that end.

The odds seem pretty low that any job or clearance requiring a polygraph would let you get by without one, even if you displayed an extensive knowledge of them and how they're flawed. Personally, if acting on principle, I'd probably just not want to work at a place like that to begin with. Of course, I'm sure there are some highly sought after individuals that could get by with that, and it probably depends on whether or not the organization you're engaging with views the polygraph seriously or as a relic on its way out.

If it were something to do with legal proceedings, I'd have to talk to a lawyer first, and see what was in my best interest.

As far as term semantics go (which I think are important), maybe "manipulating" would be a better word than "beating" or "cheating"

edit: The sibling poster also has a really good point about everyone possibly knowing it's a sham, but using it as a tool to get rid of people they want to get rid of. That might be more likely than all my speculation