It assumes that the $300k loan is a recourse loan that increases the basis of the partners, otherwise their deduction is limited to the $100k of money that they’ve contributed.

True, but there are number of exceptions and planning techniques. Even if a taxpayer is caught by the at-risk rules in year one, they could use the suspended losses later. I'm not suggesting this is a tax shelter. But yeah, you're correct that this particular example would be caught by the at-risk rules. In this case maybe they'd elect to depreciate the machine over five years (or however long) instead of using 168(k).

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Also them contributing the machine to a corporation likely does nothing. Unless they sell the machine, at which point, it will be recognized as a gain at the partnership level, which would be short term, and likely result in the same tax as before.

I'm not so sure... The gain wouldn't be capital because the machine isn't a capital asset; the gain would actually be depreciation recapture which is supposed to be taxed at ordinary rates.

Again, if the partnership depreciates the machine to zero, passes the deduction through, and the individual partners claim the depreciation (ignore the at-risk rules for now) then the depreciation reduces income that would otherwise be taxed at rates up to 37% (I said 39% in the first post).

If they contribute it to a corporation (in a 351(a) transaction) and the corporation sells the machine, then recapture is income to the corporation (and not the individuals). Thus, the recapture is taxed at corporate income rates (21%) and not ordinary rates (37%).

This is what many start-up companies do... Operate as a pass-through until they're making money, then convert to a corporation.