Maybe you can borrow one to see if you really like it.
I have several bikes: a lightweight, "fast" road bike; a tourer; a 26" mountain bike; a 29" mountain bike; an old, rigid Stumpjumper I use for a shopping bike.
I choose a bike based on the ride I'll be taking. Hands down, my favorite is the road bike. There's nothing quite as fun as zipping along on a lightweight, good-handling, properly-adjusted road bike where everything works silently like it should: shifters, derailleurs, brakes. It makes me feel like a kid - more than my other bikes.
Yes, you need a road bike.