I work for an NHS Trust too. We communicate via Text, Email, Letter and Telephone - landline or mobile. Client's choice as to preferred method.
Our number shows up as 'withheld' and we warn clients of this when they sign up for treatment.
Why might we ring instead of using other methods?
Well, for instance, a client may be on hold for a soon appointment - and if a slot becomes free an administrator will call to get someone on the waiting list booked in.
Or, the time I was taken violently ill on my way to the hospital required phone calls to my clients to cancel their appointments - texting is only used as a back up if we cannot get hold of them.
We also at times need to request more information or have further discussion with a client prior to or during treatment - we would not do this via text or email, it has to be telephone.
We avoid sending appointment letters by post as it was costing our department alone £30,000 per year. We email them instead - but guess what, they often go into 'junk mail' and people don't turn up to appointments.
To avoid missed appointments we send reminder texts to people 24 hours before their appointment. But lots still don't turn up - 'didn't get it'. So sometimes, as a clinician, I call people the day or so before their first appointment with me, to check they are coming, and know where to come (our clinic is hard to find).
In addition, we do a lot of our client work over the telephone, especially in the early stages. You'd be surprised how many clients, despite being told it will be at an allotted time, from a 'withheld number' will not answer the phone because they don't take calls from unknown numbers. We always warn them, we always text - and often also email. But it still happens.
I hardly think it is a 'system that is clearly not working'. It's pretty bloody efficient. We do all we can to reach clients in whichever way is most appropriate for them.
Consequently, if I get a call that is withheld, I assume it is NHS or similar going through a switchboard. I have never had a junk call from a withheld number, ever.