I believe what Lesley King is saying is that a standard power of appointment cannot be used to transfer assets out of the original trust to an entirely different trust. An express power to transfer assets to another trust is usually needed for that to happen. By contrast, an appointment onto bare trusts is simply a modification of the terms of the existing trust, and would be possible under the power quoted.
I’m not sure, but is the point here that the power is not itself used to transfer assets out of the trust. It is very common as you say to appoint a ‘bare’ trust of assets but the transfer of assets is still a separate supplemental exercise.
I share your confusion. I feel sure such a power could, for example, be used to create a sub-fund (such as a discretionary trust for a specific beneficiary of the original trust and his or her direct family) and that such a trust could be a separate fund - of which, for example, separate trustees could be appointed. So a transfer free of the trust fund in that sense.
I wondered if it meant “…for tax purposes…” i.e. that even if you did appoint out a separate fund, it would still be tied to the original trust when it came to calculating tax under the relevant property regime.
Even that probably wouldn’t be true if, to take your own example, the trustees appointed-out a bare trust.