but why is it deemed necessary to list some people in this way, ie not every person who dies? There must be something in this person's estate/circumstance/finances/life which requires it...
It is still done - most weeks I see similar notices in the local weekly paper. These are normally under the name of a firm of solicitors. I suspect that in cases where the solicitors (or a partner in the firm) are the legal executors it is regarded as "best practice" to advertise, as the executor has a duty to settle all liabilities of the estate. This may also apply where the executors under the will have effectively delegated the work to a legal firm, or where the executors really can't be sure they've found everything that need to be found.