After 30 years working in the field, I wholeheartedly agree: the low status of CS is indeed a huge problem among practitioners, though I doubt many 20-year-olds appreciate this.
Probably 95% of software jobs play a supporting role; the business' primary focus lies elsewhere (e.g. finance, military, advertising/marketing, health care, engineering, etc). That relegates CS and its practitioners to be a cost center rather than a profit center -- like janitors and accountants and HR -- never a star, at best a 'utility' player, a commodity. In almost all workplaces, software/IT is seen as 'the cost of doing business' -- a liability to be cost-minimized and outsourced as much as possible and then dissed by the board whenever 'players' enter the boardroom: professionals like MBAs, MDs, PhD engineers, bankers, lawyers, etc.
It's likely that the wiser more perceptive undergraduates have some inkling of CS' underclass status. It's even more likely that females and those with social and financial ambitions are aware of the limits inherent in any role where one must stick one's head inside a computer every day for, literally decades. Then at age 40-to-50, some 20 years before retirement, these software auteurs are widely regarded to be 'over the hill', and thereafter in decline until death lays them off at last. (And their job is taken by a 22-year-old.)
It's little wonder that CS doesn't attract freshmen the way honey does flies. Aside from its attractive starting wage, in too many ways a CS degree portends 2-3 decades of social isolation and indentured servitude, followed at midlife by obsolescence and oblivion.
At the end of life, is it possible that any programmer will ever look back on their days and shout, 'My greatest dream has been achieved. I have truly changed the world!'
IMHO, the answer is no. I believe THAT is why students are not flocking to CS programs. CS is not a road to significance.