Speaking as a dh of an experienced hv,
She spends the majority of her day attending case conferences, writing reports, liaising with ss, and dealing with multi-generational families of concern.
Typically, more junior HVs do the more straightforward visits.
When I ask her about some of the typical posts on here, her response is that if they're not contacting you, they probably don't have any concerns with your child's welfare. At the end of the day, they support parents with a goal of improving the welfare and outcomes for the child. If the parent has a problem with that, then they can't insist, they can only refer to other authorities.
The clinics are available to anyone who wants to go or needs support, you don't need to wait to be asked.
(sorry if this sounds goady, but genuinely it's not... I get to hear be the shoulder to cry on the stories from the other side...)