Although there is no location tag, the OP's location is in the US and many of the answers are obviouslythis has now been tagged as US-centric. However, from the UK, I can see another way of looking at this. We generally have two buckets of time off, holiday, which is paid and sick days, which are also paid but possibly at a lower rate. That means we never have the question of burning a day of holiday because of illness. If we are sick it comes out of of sickness allowance, if we are on holiday, it comes out of holiday. We are also entitled to claim back holiday if we are sick. Sick days are, broadly speaking, unlimited but holiday usually is. This is all irrespective of emergency leave and compassionate leave etc.
The point I am making is this: from my perspective, unlimited PTO is not a red-flag but in some respects, the norm. If you consider that you no longer have to sacrifice a valuable day of holiday because you have a migraine or a child\dependent needs you then it is a very useful thing to have. Yes, it can be abused but so can any system.