This is my attitude: the bag may be everywhere now, but at some point, it'll likely go back to being a less popular* bag. So if you love it, get it! Safety is a totally different story, though. Where I am, I feel like most bag robberies are targeting new bags in stores, rather than purse snatchings, but that doesn't mean they don't happen. The decision to carry or not carry a bag based on personal safety has to take into account geographic location, purpose of outing, etc.
*For the record, the Birkin is a classic and will always be popular, to some extent. But I think we can generally agree that the proliferation of H in general over the last few years is, to some extent, an influencer-driven trend. At some point, that will change, and the brand will go back to being a timeless gem, rather than a must-have for everyone with a webcam and the dream of becoming a YouTube star.