I'm a road cyclist with a bit of experience, and like most of us, without ever having been a champion, so I trust my thoughts may be useful.
If you find the position of the drops uncomfortable, this is perhaps due to your bike setup being wrong for your particular body shape. It could also be the result of a bike that is the wrong size for you, i.e., too big, forcing you to stretch too far. The shape of the bars may also be at fault, some angles suit and some don't. I've changed handlebars in the past to ensure a comfy fit. Most of your riding will be on the tops, only some in the drops. From both positions you must be able to firmly engage the brakes. You must be comfortable when riding, injury can potentially result otherwise.
Saddle position fore/aft may also be a factor in your stretch limitations.
I'd recommend seeing your local bike shop, and getting a bike fit. But remember everyone is different when it comes to flexibility, leg, arm and back length, and riding style and position preference. There are guidelines, but no one rule fits all. For example, I've got short legs, and a long back, so typically buy a frame 1-2cm larger than an otherwise a 'normal legged' person would, to get the frame length right. I compromise as a result in that my drop from the saddle to the handlebars is only 6cm instead of perhaps 8-10cm, but it helps me on hills, and is easier on my back, which at age 48, is useful as I'm not as strong or as flexible as I was when I was 22.
Once you are set up, some minor modification of your position can be found with experimentation, and some miles under your belt.
I trust this helps. All the best with the riding.