I doubt if a new bike would make much if any difference in your commute speed or time, unless your current bike just doesn't fit you right. If your bike doesn't fit, it can make riding so uncomfortable that it slows you down. That doesn't sound like your problem. You didn't mention whether your route is hilly or not, but if it's following bike paths, chances are that it isn't too hilly. So that makes it even less likely that the new bike would make you faster.

However, there are plenty of good reasons to get a new bike. You can get a new bike simply because you enjoy riding and want a better model. Or perhaps you want a second bike that provides your more versatility. There's nothing wrong with that. I've got three road bikes. One is my primary commuter, a steel lugged frame with downtube shifters and a big seatbag. I've got another steel Eddy Merckx Corsa, my favorite bike that is just fun to ride fast. And I've also got a titanium Merckx that I bought because I got a great deal on it and I knew it would fit (same size as my Corsa). It's about 1-2 pounds lighter than my steel Merckx, but I don't think it's any faster. I also like having at least two roadbikes handy in case one can't be ridden due to a flat or other maintenance issues.