I'll cut any overgrown lawn. Be it 6 inches tall or 3 feet tall. I'm confident in both mine and my machines ability and have never had a problem with overgrown lawns. I look at it as an opportunity to charge the pants off them for the possible risk, and they almost always accept because they have no choice. I've learned not to make a fuss and explain all the dangers I'm facing with possible mechanical failure to the home owner, I simply quote the job and do the work, this seems to impress them the most and land me more jobs, usually a full time mowing customer out of these properties. The trick is taking your time, mowing slowly, and removing grass as you go. Is it a pain, heck yes, but charge accordingly.
Now if the area is so overgrown it has turned into more of a brush removal job than a mowing job, that is a different story.