I've been riding on drop bars for the last 12 years in NYC, it's fine. They developed a scary reputation at a time when brake technology was shit and bike geometry was weird. This was compounded by people buying bikes used, in the wrong size, with horrible spongy brake cable housing, dried out misaligned brake pads, and throwing interruptors into the mix, usually the lowest quality garbage from back when Taiwan couldn't make anything good.
If you buy a bike that fits you, from a modern brand, with modern good quality brakes, properly set up, you're fine. Assuming you have basic bike handling skills in the first place, that is.