The military operators of our type of small turbo prop (J31) apparently use a 10 knot limit for trampling a raised arrestor gear.
Because we have different engines / propellers, we have adopted a 5 knot limit just in case.
Note that, normally, the approach cable will be DOWN: rubber grommets are pulled to the sides of the runway, therefore the cable will be flush with the runway, or even recessed into a slot in the tarmac. In this case, there will normally be no limit to the speed for crossing it.
The overrun cable is often UP: In this case, trampling it at speed may cause it to bounce up after the gear crosses it, snagging undercarriage doors or props. It's normally up, so that a military aircraft suffering brake failure on landing can simply drop the hook and snag the Rhag.
Changing from UP to DOWN normally takes about 10 minutes (ground staff have to drive out to the cable, and slide the grommets to the sides of the runway).
Cables are normally positioned about 1000 - 1500 feet in from the thresholds.
I would not aim to land, or take-off, rolling across a raised cable. And if landing beyond a raised approach cable, it may be difficult to see / judge where the cable actually is.