They may not be able to have enough people, sure, but they are still getting people.
Until recently (retired now) I worked for 18 years in an office that was mostly RN, and the problem that was most common wasn't getting youngsters in, it was retention of more middle ranks, and this was more down to some of the people in senior roles, not appreciating what they have, and many in their late 20's can earn more money outside the service.
Another issue that seemed to crop up was the lack of interesting postings, youngsters used to join to get to "see the world", now they mostly get to see "land" (mostly in barracks in the UK), and that is a government problem, because the number of ships have dramatically reduced, and that is further disrupted by the number of maintenance issues they suffer from, so often stuck in dockyards.
So my experience isn't that youngsters don't join because of modern life, more that they don't stay because it's not as good a life as it used to be.
As for the army and air force, plenty still join (and are interested in joining - hence my comment about cadet forces earlier), but similar issues occur with retention, and in recent times particularly the sort of army postings were to wars that were seen as nothing to do with our country, where the youngsters were often cannon fodder in a foreign war.
One other thing, education, youngsters used to join the forces straight from school, but now they are often expected to have (or aim for at least) higher education, including university education, and that's simply not for everyone.