I know that what you are saying is in the regs so it's official. But I don't think it's what the MLPs do, or at least some of them. And there's a good reason - the rule was never meant for publicly-traded partnerships and it doesn't address related issues.
So yes, you have a combined average basis, but that doesn't mean you have sold a ratable portion of each tranche of units you own. You still need to identify specific lots in order to have long-term or short-term reporting. You don't average the holding period, at least not in a PTP.
Last year many MLPs started showing your purchase date and original cost basis on the sales schedule attached to the K-1. (Maybe they started the year before, but I'm old and I forget.) The ones I just looked at didn't use any averaging convention - they just showed the purchase date for the lot that the MLP treated as being sold. I only looked for situations where I (or my clients) made partial sales. I think this is another situation where MLPs don't follow the rules, as they warn in the Tax Risks section. I don't know who prepares K-1s for the MLPs I looked at but it's got to be either PwC or Deloitte, I think.
And the rule shouldn't apply to MLPs anyway - it was designed for private partnerships, not situations where you can buy and sell units all year long. For instance, while the IRS says you only have 1 combined tax basis, the rule doesn't say that you average depreciation recapture over all the units you own. I have not called K-1 support in years, but in the "olden days" I did. I would give them proof of which lot of MLP units I had sold (per my broker) and they would adjust the ordinary gain to reflect the actual units I had sold. The 1 combined tax basis rule doesn't address this issue.