Do you have a desire to ride longer rides in addition to commuting? When I started commuting by bike I was riding a hybrid and I was not very fast. Soon I discovered I loved cycling and I started getting up earlier and taking "the long way" to work. It wasn't long after that when I sold the hybrid and bought a road bike. I started doing much longer rides and charity rides. The next thing I knew I was signed up on Strava and trying to beat my PRs. I guess it depends on what your motivation is and how much you enjoy cycling. I was in your same shoes, but then became addicted, and with more riding and experience my performance improved. Three years ago I was literally one of the slowest people on my commute, today I got 19 out of 2868 on one of my Strava commute segments. I think it's just a matter of what your motivation is and also experience and time. I am motivated by always improving and it sounds like that is something that motivates you. A road bike will improve your performance a little, but mostly it's about building your engine.