Cable routing through slotted hole

You are right,  your  thought experiment 100 metre slot of 4000:1 aspect ratio, would find some of the flux jumping the gap, and the inductance it would create around a pair of wires would depend on the position of the wires - However, in terms of heating the plate,  it would still be fine -  just that the magnetic field would look much the same in the very long slot, or an infinitely long one, you'd need an enormous current density in the wire to get enough field to warm up the steel. and by then the copper heating would probably be the main concern.

for a Steel of mu factor 1000, slots of a few thousand: length to width ratio are where the 'might as well be an infinite slot ' effect starts to kick in.

The other way of looking at this is how thin can the slit be in the dogbone, and I'd expect the cancellation to be starting to look less than perfect at a few hundred to one - so the un accompanied  hack saw cut of perhaps a touch under a mm wide probably ought to made a bit bigger, when it gets near a foot long.

Yes, there is a limit, but it is a long way from the normal case.

(and not all steel has a mu of 1000 either, but the low mu ones are not lossy, so there is less heating anyway...)

You are right,  your  thought experiment 100 metre slot of 4000:1 aspect ratio, would find some of the flux jumping the gap, and the inductance it would create around a pair of wires would depend on the position of the wires - However, in terms of heating the plate,  it would still be fine -  just that the magnetic field would look much the same in the very long slot, or an infinitely long one, you'd need an enormous current density in the wire to get enough field to warm up the steel. and by then the copper heating would probably be the main concern.

for a Steel of mu factor 1000, slots of a few thousand: length to width ratio are where the 'might as well be an infinite slot ' effect starts to kick in.

The other way of looking at this is how thin can the slit be in the dogbone, and I'd expect the cancellation to be starting to look less than perfect at a few hundred to one - so the un accompanied  hack saw cut of perhaps a touch under a mm wide probably ought to made a bit bigger, when it gets near a foot long.

Yes, there is a limit, but it is a long way from the normal case.

(and not all steel has a mu of 1000 either, but the low mu ones are not lossy, so there is less heating anyway...)