pan-
汎 centers on the idea of broadness or covering a wide area, as in the prefix "pan-". It suggests something that spreads out or is all-encompassing.
汎 combines 氵 (water) with 凡, which likely contributes both sound and the idea of floating or spreading broadly, as water does when it overflows.
Water (氵) spreading out everywhere like a vast flood captures the idea of "pan-" or broadness. Picture a flood covering the land far and wide.
For ハン, imagine a hand (ハン) sweeping broadly over a map, covering everything: hand -> ハン, and the gesture is all-encompassing.
generic; general purpose; all-purpose
pan-
extended hysterectomy
pervasive developmental disorder; PDD
acute generalized exanthematous pustulosis; AGEP
Pan-Asianism
Pan-Africanism
Pan-Americanism
Pan-Islamism
pan-Germanism
pan-Slavism
generalization (psychology, linguistics, etc.)
panpsychism
philanthropy
philanthropinism; educational system established by J. B. Basedow
pan-European
panlogism
artificial general intelligence; AGI
General-use JP Domain Names
general purpose computer