A centralised gov't database? There is no centralised database in the gov't. Every department has their own and to get them to share data is a challenge.
Then think of the amount of data that would be collected. How many TerraBytes would be collected in just one week. How are you going to structure it and then try and do any kind of data mining. Currently just between Canada & the US there are millions of commercial crossings and tens of thousands of traveler crossings per day. The border agencies (CBSA & CBP) need to validate and screen these passages. Already a tonne of data to process. I can't imagine adding every other type of movement and transaction to that. Thinking of the scale and volume of data I just don't think the current infrastructure of government agencies can do this.
And as for the benefit of EDL, it's a volunteer (you have to want to sign up for it) program where extra screening is performed to validate citizenship. This involves the collection of extra data beyond that of the regular driver's license. Now suppose you want to keep that data only in Canada, how do you propose to perform real time (when the car is at the booth) secure lookup into the Canadian database? The CBSA doesn't have this data from what I read, it is the province. Are the US CBP going to be willing to hit each province's database to retrieve info (probably a photo & basic tombstone data). Expensive and complex (different protocols, databases, etc.) and I can't see a transaction like that happening in fewer then 10 seconds. That's increasing the border wait times which are already slow. This is a pilot program (when you read a select group of 500) so at least give it a try and see if it works. The privacy commission is there to make sure our rights are protected, put a little faith / trust that they may get it right.