It would be very difficult to sweep away ALL the barriers to trade among the provinces. It is the provinces that set the standards for licencing of professionals and qualification of tradespeople. Unless and until the provinces all have the same standards, there will be problems in getting credentials from one province accepted in the other provinces. 

Similar issues apply, in many cases, to goods. The provinces set standards for what can be sold in the province, so even if it's legal for you to bring a non-conforming whatsit from another province, it may not be legal for a retailer in your province to sell the same non-conforming whatsit.