Considering that the CA has two hands occupied taxiing, I'm surprised there's any airline that doesn't have the FO do the announcement.
I'd like to thank the OP for making the recommendation. Before last month I, for one, hadn't considered that adding on a few words could be an issue.
The FACT is that last month on a line check the Check Airman specifically mentioned not to extend the announcement unless the parking brake is set.
The FACT is that a Fed told him that he didn't like it that we were regularly breaking this rule. That means that if we didn't cut it out soon then someone would be made an example of.
If you don't mind being the one they make an example of then Go Ahead and disregard an honest heads-up.