Would it make sense to buy a fund like this, and reinvest all dividends and capital gains in order to grow an income stream? What wouldn't seem to make sense would be to receive payouts which might consist of (at least in part) of your own initial investment. If so, then you would be reinvesting your own initial investment, and perhaps paying tax on it as well. Maybe this type of fund would only make sense if you are using the income distributed immediately?
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(That latter objective depends on the payout strategy. For example, Fidelity's Income Replacement Funds are designed to spend down to zero, much like a fixed term annuity.)
The emphasis is on low volatility and cash generation, not exactly what one wants if one is trying to grow assets for a later income stream. One doesn't invest in bonds (and reinvest interest) for capital growth.
Managed payout funds are fairly common in the closed end fund universe, so you might look around there to see how they work. Return of principal is tax free - you don't have to worry about paying taxes on your own money. The more interesting question is what happens when the investment generates more income and gains than the fund is scheduled to pay out?
A fund is taxed directly if it doesn't pay out substantially all its capital gains. According to the fund's SAI, Vanguard gets around this by some legerdemain that makes it appear to the IRS that you did get paid the gains, and then Vanguard gets you an offsetting tax credit. You don't have to worry about the details; the short story is you don't have to worry too much about weird tax impacts.
Here's an interesting and fairly current discussion/analysis of managed payout funds from Natixis and Vanguard. For a variety of reasons, including the way Vanguard gently adjusts the payout percentage based on performance, I like Vanguard's approach. But it doesn't seem to fit your objective.