I have to say it highlights a fundamental misunderstanding of what FOM is about. Just granting visas for the sake of it sounds puerile, like we don't like YOU (to other Europeans) let's be pals with YOU over there.
I don't think it's about 'we like you' or 'we don't like you' or brushing aside our historic ties with European nations. It's true that we've had treaties and allegiances with some of them for centuries, but Australia, NZ and Canada are part of the Commonwealth. They're nations that have a much stronger tie to us than France or Germany or Poland has ever had. Our monarch is their monarch, they're former territories of the British Empire. Their populations are made up of significant numbers of people who emigrated to those countries from the UK and so there are millions of Brits who continue to have close family ties to one or more of those nations.
And there is the reason I stated above - that these nations are a lot like us from an economic and a standard of living viewpoint - so they're nations we can have an equal relationship with. Unlike countries in Eastern Europe, where we are the wealthier partner who attracted large numbers of people to come here, chances are that that won't happen with Australian, NZ and Canada. Instead, our populations will be free to go and back forth without significant numbers permanently moving in just one direction. India is not an equal partner in the same way, nor is there a sizeable population of former Britons residing there. It would be another unequal relationship of the type Britain wouldn't want post-Brexit. A major reason for Brexit is the huge number of people who have arrived here recently. Any government going forward is going to be eager to avoid that situation repeating, as it's not a vote winner!