Hume claims he feels a natural compulsion to do philosophy, and that doing it brings him pleasure. He admits that he feels the practice of philosophy improves human affairs, but is careful to insist that he does philosophy because he wants to, and enjoys it, and not because he "ought to."
One might well accuse him of being disingenuous with this answer, but he's clearly aware of the issue you mention, and trying to address it.
A Treatise of Human Nature 14.7.12
At the time, therefore, that I am tir’d with amusement and company, and have indulg’d a reverie in my chamber, or in a solitary walk by a river-side, I feel my mind all collected within itself, and am naturally inclin’d to carry my view into all those subjects, about which I have met with so many disputes in the course of my reading and conversation. I cannot forbear having a curiosity to be acquainted with the principles of moral good and evil, the nature and foundation of government, and the cause of those several passions and inclinations, which actuate and govern me. I am uneasy to think I approve of one object, and disapprove of another; call one thing beautiful, and another deform’d; decide concerning truth and falshood, reason and folly, without knowing upon what principles I proceed. I am concern’d for the condition of the learned world, which lies under such a deplorable ignorance in all these particulars. I feel an ambition to arise in me of contributing to the instruction of mankind, and of acquiring a name by my inventions and discoveries. These sentiments spring up naturally in my present disposition; and shou’d I endeavour to banish them, by attaching myself to any other business or diversion, I feel I shou’d be a loser in point of pleasure; and this is the origin of my philosophy.
An Enquiry concerning Human Understanding 1.9
And though a philosopher may live remote from business, the genius of philosophy, if carefully cultivated by several, must gradually diffuse itself throughout the whole society, and bestow a similar correctness on every art and calling. The politician will acquire greater foresight and subtility, in the subdividing and balancing of power; the lawyer more method and finer principles in his reasonings; and the general more regularity in his discipline, and more caution in his plans and operations. The stability of modern governments above the ancient, and the accuracy of modern philosophy, have improved, and probably will still improve, by similar gradations.
Were there no advantage to be reaped from these studies, beyond the gratification of an innocent curiosity, yet ought not even this to be despised; as being one accession to those few safe and harmless pleasures, which are bestowed on human race.
This article may be of interest, I relied heavily on it in crafting this answer.