I have a PhD. Some time ago I did the experiment of calling myself 'Doctor' in various (external, public but non-professional) situations, to see if it made any difference to how I was treated.
Mostly, no difference at all. Occasionally, people treated me a little less well, probably on the basis of 'He's a bit up himself, isn't he?' Fair enough, really.
So I stopped calling myself 'Doctor'. Except in one particular set of circumstances, where I was treated better, listened to more, taken more seriously: this was in circumstances around healthcare. I rationalised this result on the basis that people working in healthcare are used to being told what to do by old men called 'Doctor'.
I told my children this, after one of my daughters complained in conversation about being patronised by a (male) paediatrician. (My children all have PhDs too, a stealthy boast if you like.) Such patronising behaviour, it seems, is not uncommon.
Anyway, my daughters, in particular when young(ish) mothers, found the same thing I had; possibly even more so. Talked down to, patronised when 'Mrs' or 'Ms' (they have different takes on marriage and consequential female titles), treated as just-another-know-nothing-mummy, they found their concerns about their own health and that of their children taken much more into account, and with more seriousness, when they changed to being 'Dr'. This, in several different countries, but including NHS in UK.
Sad, perhaps. But true. Make of it what you will.