I don't mean that the solutions to these problems are similar to the solutions to version control problems in software, I'm just making an analogy. Version control is a tricky business and has evolved over time, and it's that evolution that I'm referring to.
And I did mean "totally possible" in the sense you indicate, that is, technically possible, but far from a solved solution (after all, I'm not quitting my day job to start offering this as a service). The historical reason for a payday is that cash is hard to move, so the armored car would swing by and people would line up for money; later banks would do the same thing. Because "paydays" and "paystubs" exist, other processes and organizations latched on to them as a standard place to add more process, so "running payroll" became a more and more complicated beast, thus making it even harder to make it an incremental process.
So the first barrier is now gone -- while some segments of the population are cash-heavy, modern inter-bank transfers and the rise of electronic payment systems mean that banks can easily handle the cash outlays necessary to support the demand for physical specie out of cash on hand (not to mention improvements in modeling that allow them to anticipate cash demand).
But the rest of the "hanger-ons" are not even close to being able to support this; everything from landlords asking for paystubs, to how payroll taxes are handled, to the way that benefits (like health insurance or retirement plans) are calculated, to the way that non-direct-payroll services like phone bills and cable bills are calculated, and the idea of limits on services (data, etc.) that are metered on a sliding monthly window instead of a continuous rolling window mean that it would be very difficult to do effective planning, unless all services started adopting these methods.
To actually allow people to do this you'd almost need to have intermediate services -- a "cell phone account" that gets funded, say, daily, and remits payments to the cell phone provider on a monthly basis. Similarly a "rent account", and so on, that would gradually allow you to get an idea of what your actual cash flow looks like, without having to deal with periodic shocks that represent lump outlays and receipts.
For now it's just an interesting thought that the foundation that the concept of "payday" is build on has turned to sand, and the question is whether we can find a way to take advantage of this new flexibility. Yudkowsky's tweet addresses one possible way that this may provide a benefit, and it's interesting food for thought even though I'm not completely convinced.