One of the jobs of Methodist travelling preachers used to be to visit families in their homes and check up on them. As with all things, John Wesley provided some specific advice on how best to proceed.
The preacher should take the children aside and find out how well they have memorized the “Instructions for Children,” which would have been left to the family before. Then, the preacher would pull aside each family member for private one-to-one conferences. In these, the preacher would test the person’s knowledge of the basics of the faith and inquire about the progress of their souls. Instruction, advice, and reproof would be offered as needed.
I’ll confess right now, I’ve never done anything remotely like this.
But I see its value. Elders in the United Methodist Church are charged to teach house-to-house still.
The preacher today probably does not have the authority to conduct himself or herself in this manner. And many would argue that such an approach would be too authoritarian even if it were possible. But the practice does make me wonder how well we monitor and discern the knowledge and spiritual vigor of the souls – to use the old phrase – “entrusted to our care.”
My observation is that much of this kind of discernment take the form of of informal and laity-instigated contact.
Is there room for anything like the old pastoral visits that Wesley and Richard Baxter before him envisioned?
I am a part-time local pastor serving 
The doctrine of original sin is surely more humbling to man than the opposite: And I know not what honour we can pay to God, if we think man came out of His hands in the condition wherein he is now.
I have to confess that this kind of visit makes me very nervous. It reminds me of my Victorian Prussian teachers in Lutheran school who, out of nowhere (e.g. a grammar question during the math lesson) would pop a question at you and expect an immediate right answer or you would get punished. I can tell you that all it did was to make me feel inadequate and anxious.
I have no idea what the cultural context of this was although I do know that, in America in the 18th century, many States also mandated such teaching and it was seen as part of basic literacy. Reading full stop and reading the bible went hand in hand and it wouldn’t surprise me at all if Wesley and Baxter intended these things in the wider context. One of Wesley’s missions was to raise up the illiterate poor into literate, respectable working classes.
You do still see a vestige of this in the UK, though. Pastoral visits by the minister, initiated by him or her, are an expected part of the job. In some places, at least one such pastor-initiated visit is expected to every household in the church in the first two years of a minister’s appointment. And the pastor is expected to come around once a quarter to visit and give comfort and communion to those who are shut-in.