And that's safe and OK. I had the impression the goal was to do a
"real" check of the disk which requires reading-writing-reading
(or letting the disk itself report any error(s) if one's doing
reading only) to assure data integrity in each sector.

Modern disk surfaces are extremely tough and I haven't seen a
head crash or sector data failure in at least over a decade. What
usually fails after 3-5 years nowadays is the flexible wiring from
the head/arm assembly to the disk's internal controller from being
flexed too many times (e.g., arm motion).

Some OSs actually track arm motion and power-on hours and gradually
downgrade the rating of a disk over time and proactively suggest a
replacement disk when the values exceeds a certain threshold. The
point being to replace a disk _just_ before its projected failure,
and the algorithms are extremely good in that regards.

You really don't want to be in a situation requiring the use of a
disk recovery service -- the pricing is astronomical. Backup, backup
and backup your data.