These used to just be private, cash-flow heavy companies that paid dividends/distributions. They still are, to some extent. The flexibility to increase or decrease the dividend depending on market conditions is what can enable them to survive during a downturn. In that respect, public upstream MLPs were too rigid.
I think patient private capital is the answer here. Something cash-flowing so much is severely limited on the upside, but is also very protected on the downside. Lots of cash flow with aggressive hedging, moderate leverage, and some low-risk development is a nice business model. A pension fund or endowment should be all over that asset. Buy the asset, pay out dividends when appropriate, re-invest cash flow when appropriate, pay down debt when appropriate, lever up where appropriate, and finally, exit when appropriate. It's not a tough business model but the lack of patient capital is definitely an issue.