Not a week goes by on Global Custodian[0] headlines for technology that mentions at least a couple well established firms using blockchain for securities of all sorts.

Whether I agree with these developments or not is completely irrelevant. I'll personally stick to pursing a market neutral strategy and exploiting intraday ETF discrepancies for now.

[0] https://www.globalcustodian.com/news/technology/

Harbor and Polymath are working on tokens which can accomplish all those things. The claim is that tokenized securities can reduce the number of middlemen needed to issue new securities, so shares could be traded on individual apartment buildings, etc. Nobody thinks moving Apple stock to a blockchain would change much.

I’m not advocating this argument, just relaying it since you asked.

If someone can honestly explain why the blockchain would be any better than the DTCC for tracking equity security ownership I'd love to hear about it.

Because it allows people anywhere to access the aforementioned security. It also has a lot lower friction for all the participants.

People can access a security today, anywhere. By using their broker over the internet.

Can you give specific, real-world examples about how the "friction" is lower? And what precisely do you mean by "friction" - lower cost? ease of use? something else?

Only if you are using a very narrow definition of "people", "anywhere" and "security".

I am in Argentina. I can make a VC-style investment on a company being founded in Europe tomorrow and resell my shares 3 months from now to another investor in Australia with no middlemen, brokers, filings, etc.

That just didn't work before. It would have been impossible for me to do that. Its also more risky in terms of regulatory protection, of course. But in any scenario ICOs are huge disruption for the VC industry, and if the crypto market matures, I expect that to expand into other spaces.

Specific instances of friction: transferring funds, assigning shares, lack of liquidity of both shares and secondary markets (or, quite simply, lack of markets).

I guess that Overstock guy wants to blockchain equities so that people can't naked short his company.

People already can't naked short sell except in very limited circumstances for market making purposes. It's not as widespread as you think it is. I would suggest reading about Regulation SHO.