I would hope that my answer is the same as everyone elses: Absolutely.
The starter is there for that reason: He/she is your starting Pokemon. They're supposed to be there to get you started and help you rise to fame and fortune.
But once you begin battling competitively you'll probably abandon it because there will be better options. However, sometimes you really do want that Blakizen as a sweeper or that Infernape as a beat-machine. It's all a matter of preference. But yeah, I absolutely keep my starter with me.