It's always difficult when people regard mobiles as only for them to actively use, and don't stop to think about people who might need to get in touch with them. It doesn't help with all the scummy parasite scammers who seem to make most of the calls that many of us receive these days.
It's definitely a mindset - and a vicious circle, because people don't call or text them as they know they won't have their phone turned on and/or get the message; so from their point of view, they rarely get a call or a message, so why on earth would they need to ensure that it's always turned on, at hand and frequently checked?!
It might be slightly devious, but is there something that you know they really like and would want to know/have, that you could call or message them about quite regularly (not bombarding them, of course)? Special offers, events, useful local information, specific kinds of news, weather - the kind of thing that they might be disappointed to have missed out on, and realise that they never needed to miss thanks to their wonderful phones?!
I think that might be the only way to make them change their mindset to viewing their phones as positive, useful things that can keep them connected, enhance their everyday lives and bring them interesting info - especially that other people/sources bring to them, and maybe with a time-limited validity; rather than just as emergency communication devices that they keep switched off and then, only IF they feel they need to make a call urgently, they have to look for, switch on and then realise that the battery has died anyway.
If they can at least get into the habit of making sure that they're left on, kept charged and carried with them, they can use them as much or as little as they want/need; BUT crucially get it fixed in their minds that they need to be able to receive calls and messages as well as just make/send them.
Make sure that they have all the contacts of family and friends that they might need and, ideally, help them to set a different ringtone(s) (for standard calls/WhatsApp/message notifications etc.) for them instead of their default/normal one - that way, even if they do end up getting bothered by unknown numbers that they choose to ignore (as indeed do many of us who are very tech savvy), they can know that, every time their phones start playing their favourite song or a burst of a familiar special sound, it means that it's a loved one whom they (presumably) DO want to speak to or otherwise hear from.