I’ve been riding a dropper for a decade and would never want to ride the road without it. Just like the advantages in MTB with descending and cornering; on the road you get those same advantages. It also makes the ride more enjoyable because of the added confidence, while it shakes up your muscles allowing you to use your quads more and spin easier when it’s lower, and stretch out and lug more when it’s higher.
The main benefit to me though is climbing. I even set the dropper at hyperextension height. Riding this high all the time would cause problems, but for a few seconds it feels great and totally stretches your legs out, while it can even help to stave off cramps. But also when climbing you can put it to the same height and sit on the very tip of the saddle in a “perched” position ( I use an Adamo TT saddle for comfort) It becomes, essentially, a virtual standing position. It’s not necessarily better or faster than the standard sitting and standing climbing positions (both used my most riders at different times.) What it does though is offer a real 3rd positioning option utilizing different muscles than the standard two.
The bike is also more efficient when your weight is balanced between the wheels, which the perched position gives you, similar to standing. It also allows you to stay on top of the gear, so when you crest a hill it feels like you are able to recover and get up to speed faster.