More precise (sensible, sensitive) server monitoring score

You can’t rule that out, as only with HW-stamping you know when the package was received and send by the NIC. As most don’t have HW-stamping it’s the kernel doing the stamping.
That time is higher then the NIC doing it, so processing can’t be excluded.

More then an average guess at best. It really doesn’t have much meaning other then showing a route is poor/bad/good at best.

A stable path at 100ms (via e.g. sat) is far better then a wobbly path of 10ms one second and 1000ms the next. As I presume it will also show in the time-accuracy.

Maybe a min/max RTT should be given, so you can see how stable it is, with an average value to see the middle-value. Because if min/max are wide apart, it makes it an unstable path (unless you did it yourself, reboots, testing etc).