Pet projects by any department that aren't in the interests of the company should be discouraged.
Especially by HR, because unlike an engineering pet project that may waste some time, pet projects by HR can significantly impact the quality of life of every employee at the company, cause people not to join the company or quit the company, and so on.
Dysfunctional HR (which is almost all HR) is just about as bad as having a thieving dishonest CFO or a clueless visionless CEO, in terms of its impact on company prospects.
In comparison, a designer who does their work ever so slightly better than is actually going to have business value, or an engineer who puts 10% of their time into some project that they incorrectly think will help the company, or who chooses the 2nd best tool instead of the 1st best tool because the 2nd best one will look better on their resume, these are all much less significant to the company or to their coworkers.