I too find Peter’s above-quoted remarks compelling and I strongly endorse them.
But you are keeping me on too short a leash, Pen! Please acknowledge the difference between a discussion of the motivation, setup and legitimacy of my approach on the one hand, and its implementation on the other. In the implementation of the HP I have to delve into hard-core set theory, including issues involving HOD and indiscernibles which, although surely not as difficult to appreciate as Ultimate-L, are nevertheless demanding of a strong knowledge of set theory. The IMH may be readily understandable to a set theory bonehead, but it is too much to expect that #-generation or the proper treatment of class-genericity are immediately and “generally understandable”. Otherwise put: it is too much to expect that to uncover the real meaning of “maximality in height and width” that we are bound to explaining every move to our grandparents. Why should everything in the implementation of the HP lie at the surface of set theory? Maximality is to be viewed as intrinsic, but the tools needed to understand it come from set-theoretic practice, even though there is no “extrinsic justification” involved.