"This ignores that other space craft on reentry... using your aerobraking method have to take similar stresses."
No, they do not. The heating occurs due to compression in a detached shock in front of the vehicle. Much of it is radiated away immediately, the vast bulk of the remainder is left far behind the craft, and the craft itself only needs to handle a tiny fraction of it.
"You say it will meet with the impact of a tank shell. But we're talking about brushing the surface not impacting it at a 90 degree angle. The translated energy will be vastly lower."
No. The energy is a function of the relative velocity. The angle is completely irrelevant. You are converting the kinetic energy of the cable and spacecraft into heating of the cable and ground via friction, and the cable alone has enough kinetic energy to completely destroy it.
"The issue will be can the surface withstand the friction and heat. A surface similar to diamond should withstand the friction."
Apart from the fact that a hypothetical diamond super-cable isn't a substitute for the present reality of aerobraking...it would not, and the surface of the moon isn't perfectly smooth diamond. Your cable will make first contact with projections such as mountains, hills, boulders, crater edges, etc. It will separate explosively at the point of contact and the portion below will slam into the side of whatever the obstruction was. It may remove the obstruction in the process, but that's of no help in braking your spacecraft. This might be a useful method of landing on very low gravity objects...providing both a deceleration method and a way of securing the payload to the surface...but the idea is completely unworkable at the speeds involved in landing on the moon.
You might be able to engineer a hypervelocity runway landing, a very smooth aluminum surface with a cushion of injected gas to support the craft and electromagnetic braking to reduce velocity until you can make physical contact and stop, or you might be able to put up a lunar space elevator or surround it with momentum exchange tethers, but this gets back to the infrastructure problem, and it might well be cheaper to just land on rockets.