I use an old rock climbing 11MM Bluewater dynamic rope and a 9.xmm Bluewater static for some of my rigging. I also have some new "arborist" ropes, most specifically designed for the arborist trade. In my limited experience, I've found the "rock" ropes work well and take a lot of abuse.
The dynamic quality of the rope, when used with natural crotch rigging, or a block, seems fine. Keep in mind rock climbing's "fall factor (fall distance/ length of rope = distance of fall divided by length of energy absorbing rope from anchor to load)". If natural crotch rigging, the distance from the crotch to the load is the effective length of rope absorbing energy. Therefore, the "fall factor" always the maximum encountered in any rock climbing experience where the maximum fall factor is 2:1 (or just "2"). Couple that with a "soft"/"running" catch.
Keep in mind that the kernmantle construction has roughly 15-20% strength in the visible sheath/ kern, and 80-85% strength in the non-visible/ non-inspectable core/ mantle.
All things require judgment. Rock ropes are looking at loads of usually less than 200 pound masses, moving larger distances and at higher speeds. "Soft catches" by the groundmen reduce force as well.
I like to use my old ropes for non-critical catches, as I'm cautious, more than I'm afraid something is going to break. If I had a big limb over a house versus over some flowers, I'll probably go with modern arborist standards and equipment, which hasn't been put through lots of work and dirt/ bark/ grit.
Keep in mind that "fall ratings" on ropes do not mean that the rope breaks after "6" or "9" lead falls (all having their own individual "impact forces". The ropes will lose elasticity over time. The climbers' bodies absorb more of the load. Climbers aren't allowed to "run" until just shy of the roof/ landscaping/ obstacles either.
I've not heard of ropes breaking. I have heard of large loads dropped on old "rock" ropes, without fail. Anecdotal evidence, for sure. People would look funny at you at a rock climbing area if you were top-roping on an arborist's rope if they didn't know that it was surprisingly strong, and not just some hardware store rope.
In all things, judgment is critical. Also, consider if something goes wrong, will the insurance company cover damage from non-industry specific equipment. Be Safe and Cover Your A**.