First and foremost this is about safety. I know there are some lifestylers out there who claim to not use safewords but, if you question them closely, you actually find that they use something similar or have an alternative method to ensure the safety of the sub.
I think 'safewords' have been associated too much with 'play' or 'tourists' and with roleplay scenarios rather than what some may call 'proper BDSM' and this is why some hardcore lifestylers do not use them - for fear of being associated with these tourists.
This is fair enough - you want to dissociate from something which is considered undesireable. However, you still need to consider safety and respect of the sub. Unfortunately, some inexperienced idiots also try the 'no safewords' pose but without the consideration of alternative safety precautions. LCslave's point about being offered the choice shows good practise in my view, though I also assume that the Lady in question also keeps a close eye on her subs who choose not to have a safeword.
A safeword is a useful tool which can be very handy when you do not know any or all of the people you are playing with well enough to judge thier reactions to certain acts. Some couples eventually find they no longer need it because they know each other so well but still have it 'just in case'.
Of course, on the negative side to a safeword, one thing I have noticed is that sometimes when you have a safeword you may actually push yourself more than if you didn't have one. The fact you have an out means that you will take more punishment simply to not use the safeword. It sounds paradoxical but I have noticed it in myself a few times.