They would actually. AIUI they just wanted Canada to wait until production had reached a level that it could reasonably be expected to replace in service rifles before they would free up the production staff. Canada had skipped out on the last update (to the Long Lee) and was therefore equipped largely with Martini’s. So they felt they really needed an update soon. And in came Ross promising a home built rifle better and faster than the British could deliver anyway. And promising it could still be made in the same calibre as British weapons. With the support of Hughes as Minister of Militia, he got the contract.The whole reason the Ross existed is the Brits wouldn't license the SMLE to Canada for some reason
When British production caught up they were happy to expand it to the Dominions. New Zealand and Australia both got a factory. But by then Canada was committed to the Ross.