I don't think this is true. It's something Musk likes to say, but a source would be useful.

I'm sure the launch costs (which can be worked into $/kg for payload) can be easily looked up, and show that SpaceX's reused rockets are much cheaper than what came before.

Do you have a source?

We haven't seen a reduction in space insurance premiums of any particularly large magnitude which I would expect if the costs of launching satellites into space had been substantially reduced.

Falcon 9 is as cheap as Proton M according to something google found somewhere.

SpaceX is a small fraction of total lifts though.

Something like 20-25% of all launchs globally doesn't seem like a small fraction.