GDP might be the ultimate example of Goodhart's Law: https://en.wikipedia.org/wiki/Goodhart%27s_law
The typical example is: hospital emergency room wait times were made a "target" and therefore hospitals stopped admitting ambulances (literally having them circling around the block) before they had the staff freed up. But there's nothing wrong with emergency room wait times being kept low. The obvious locus of evaluation, however, was moved from the patient (who is evaluating his whole end-to-end emergency care on many metrics, including but not limited to emergency room wait time) to some bureaucrat who assesses the hospital only on the wait time.
I recommend being clear about which definition is used, rather than trying to enforce one meaning should always be used.
A classic example would be a company which outcompetes its rivals by working around regulation that companies in that sector are subject to. That enables it to gain a competitive advantage within the system it's operating in, but is pessimisation rather than an optimisation when looking at the bigger picture and longer timescales.
In fairness though, if a politician stands at a stump and says, "see, I'm doing great with GDP", but it's because they've been serving the metric rather than the underlying principles, they're likely not going to be well received.
The solution is to not base policy on indicators but politics needs to keep things simple.
In my first Economics subject in high school they told us to never look at unemployment without looking at the participation rate with it.