It's been tried, half-heartedly, in the past. I was on an opening of parliament when 3RCR provided the guard. The fact of the matter is that Petawawa views Ottawa ceremonial taskings as a burden not laid on other bases, and many of our other major bases are too far for road moves, making the cost of hotels and airlift excessive.
There has been some talk kicked about about having a standing Public Duties unit in the NCR -- the rotating task for the Tomb of the Unknown Soldier may be the first step toward this. And there would be no reason to shut down the clearly successful Army Reserve summer program -- thanks to the double fists of Posting Season and Summer Leave the Regular Force tends to lose a lot of capacity over the summer months.
On the whole, I think it's overdue. I think pulling Geo Techs and Comm Researchers off of their primary duty at short notice and putting them on parade, not because their current task is low priority, but because they are a Cpl/MCpl in the NCR is a silly way to allocate scarce resources. But a standing Public Duties unit would need infrastructure, and infrastructure in the NCR seems to be an ongoing drama.