I have noticed that the maker recommends using a single radial with the budistick, as it is easier to fine tune the antenna when it is in lazy L dipole format than when you have 3 or 4 radials to tune, or need to adjust the vertical element.
However I understand that in such configurations, half the antenna current is flowing in the single radial and unless it is elevated, that half of the tx power is split between being radiated and being absorbed by the nearby ground, rocks, foliage etc, While the antenna impedance may well be adjustable to be a close match to 50 ohms, or is at least non reactive, that doesn’t necessarily translate into best radiation efficiency. Part of the radiation resistance is the loss resistance in the nearby ground, so exposing the antenna to that loss is undesirable.
While it is tempting to simplify a vertical antenna’s ground system to a single radial, and it looks good on an analyser or on the swr meter, using two or more elevated radials is better for dx and produces more radiated signal.
Perhaps one of the wspr-aided antenna comparisons will confirm that in due course.