What should they be doing? I share the frustration: Crew don't like being ignored any more than anybody else, but the question remains - What should they do?
Should you pursue every miscreant under a zero tolerance regime? This will result in arguments (lots of them) and loud ones in front of everybody. It's not a good look. What if the passenger simply ignores you, or refuses to comply. What can you do then? Threatening to report somebody to the authorities only works with some people and simply antagonises those who don't care. It also creates an unpleasant cabin atmosphere for the other passengers, who will of course be delayed on arrival while the authorities do their authority thing.
Tu.114 has given the company line about support for the crew. The truth is that many airlines will side with a customer instinctively: Crew are involved in a witch hunt before they can turn round and there is a long list of people eager to pass judgement on how things should have been handled better (not the least here on PPRuNe). The courts are notoriously lax on pursuing and punishing aviation related crimes. Naturally, this isn't the case on this website, but there are a surprising number of people who really don't like Cabin Crew at all - sometimes with justification.
So there you go. You can tell people to do something on the PA, repeat it in person, check that it is being done and then that's it. If they choose to do otherwise subsequently, there is very little that you can do: Crew are adults and so are passengers. You can only do so much.