Do we agree that deflation can make it harder for capital to be profitable?
Yes, but you have the cause and effect precisely backwards.
Not sure how we agree then.
You're assuming you can hold the monetary system constant as you imagine various changes in economic productivity. But the monetary system responds to the economy.
AND the other way around. The economy responds to the monetary system. What we're discussing is how price deflation (an indicator in the monetary system) affects investments and therefore the economy. And most people here are saying "Deflation doesn't affect real investments negatively at all, if anything, deflation is good for the economy". If I try to make the examples with "two parallel and identical economies but only changing the deflation rate" is to make things simple. Not that I actually think that is possible. I know that the economy is a complex system with no isolated parts. I know that if the two economies were actually identical, they would present an identical deflation rate. The question still is, does deflation discourage the production of new real capital (production goods)?
If so, is it only as the expense of a shift to consumption?
If so, how is that shift to consumption justified?
For example, Bitcoins can become scarce because of their built-in scarcity. But they can also become scarce because demand goes up due to economic productivity. And either way, the result will be in increased effective supply of Bitcoins in the form of things like demand notes, mortgages, or bonds circulating as currency.
Are you saying that deflation will be naturally postponed while the system accepts more credit/debt that can act as a substitute? I didn't had the courage to say something similar myself, but actually I think that the credit cycles are caused by the basic interest making the credit substitutes grow exponentially. Back to the claim I think you're making...
If deflation is postponed while the system accepts more credit/debt, eventually the credit won't be able to grow more and there you have the cycle bust. With the "not anymore postpone-able" deflation accelerating the unavoidable credit destruction process. Until the level of debt is "sustainable" again.
What will happen, unless you imagine a coercive government mucking with the process (say by printing currency, borrowing endlessly, or strong arming interest rates), is that the economy will drive the currency to encourage sensible investment, or non-investment, as makes sense.
You seem to be saying that if resources are not going to investment, they have to be going to consumption for a good reason.
What concerns me is not that "resources are spent on consumption" or "resources are spent on investment". Is "resources aren't spent on consumption nor on investment". Because there are resources like food and labor that happen to irreversibly disappear if not used at a certain time.
Take into account that I'm not attacking here the free market. I attribute these problems to the gold standard, for example. Which is not an intrinsic part of the free market, a free monetary market is. Bitcoin as an only currency would suffer the same problems, but I don't fear a "bitcoin standard" to be enforced. I also think that the Keynesian solution of government spending is just a bad patch that creates more problems without really solving anything, only postponing things. But yet they acknowledge there's a problem to be solved.
The point is that if the price of the money in that community is rising and is expected to continue to do so (probably you need collapsing credit/debt for that), people will prefer to keep the money over buying the closed factories and put them to work again. But, yes, at some point (when the deflation has destroyed enough credit/debt) that will stop, the financial market will get restored, real investments will resume and the factories will be reopened.
I don't think deflation is the problem per se, it's just one of the symptoms and the natural (but destructive) solution and unavoidable conclusion (well, there's also hyperinflation to the debt jubilee by destruction of the currency, but that doesn't deserve to be called a solution) of credit/debt cycles.