"But isn't the difference between my new reduced basis and the amount I sell shares for considered a capital gain?"
Nope. Very roughly, the component that comes from increase in unit price since your purchase is capital gain, while the portion that comes from reduction of basis due to distributions is recaptured as ordinary income. It is not the same as selling a stock. If you have held for a number of years the deferred taxes can be very significant. And if you only sell a portion rather than all of your position it is even worse since that will not unlock passive losses which will offset some of the taxable income.