I can roughly see the relationship but not smart enough to see immediately what it means without more thought. FWIW AFAIU the broken window parable is itself not without controversy.
Well you've flipped now to discussing the definition of useful, no?
First, gold is plenty useful outside value store: only ~30% of new gold per year is used for investment (this is per GS in 2015, I believe, and this is unlikely to have changed significantly one way or the other, pls feel free to correct me). The majority of remaining is used in mainly in jewelry & electronics (again per same source).
Second, on its way to providing for the point above, it employs hundreds of thousands of people full time that take that money to spend, save, invest aka. it works in the economy.
I'm not saying that bitcoin can't function like this or some similar way in the future, but it's a fact that it doesn't right now, and per this criteria I would say it's both more wasteful & less useful than gold. Bitcoin is simply plugged into your outlet right now and quite literally wasting energy unless you're using it to heat your home. That people have assigned value to the record of energy being spent is a separate phenomenon IMO.
I've always found it hilarious that block rewards are the literal definition of Keynesian stimulus - "burying money in bottles in the desert and paying people to dig it up". Early-stage cryptocurrencies are effectively economies where near-100% of employment rests on government employment.
People just think it's totally different, because this time they are the government. And because cryptocurrency is so steeped in libertarian ideology, they are unable to acknowledge any of the lessons of traditional economics, and are thus doomed to repeat its mistakes (eg: deflationary/hyperdeflationary currencies).
As a form of Keynesian stimulus, it's totally possible for block rewards to represent a net positive gain of economic activity as they "prime the pump". Gold mining is probably quite mechanized nowadays, so I wouldn't really care to guess which is more efficient at translating stimulus into economic activity, though.