Not an american thing, but rather old-fashioned. A long time ago, well-to-do Britons had a "family lawyer". Not on retainer; but he knew the family business (so didn't need briefing), and he dealt with wills, property, that kind of thing. Like a family doctor, rather than a specialist consultant.

Nowadays only the very rich can claim to have a "family lawyer".

My middle class family certainly has a "family lawyer" who deals with wills, property, that kind of thing. You should use a lawyer for those things, why not use one you know and trust?

If we were very wealthy, perhaps we'd have a legal matter for him every month instead of every year or two, but that's plenty of time to build up a relationship. Similar to having a family doctor.

Some people do but usually the "have your lawyer" phrase means "find a lawyer who specializes in this area and contact them". Still, the point still stands, it's expensive and time consuming to even begin the process of engaging an attorney if you haven't done so before.

Say "have a lawyer" instead of your lawyer would convey that point without that baggage of someone sounding like they don't understand that most people don't already have a lawyer in the same way they have a dentist.