"how about "half", the exact word that 'hafu' is supposed to emulate?"

And in Tokyo Dialect, the 'フ' ('fu') in 'ハーフ' ('haafu') has its 'u' muted to silent or near-silent so the pronunciation is nearly identical to English 'half'.

It's practically an identical borrowing in both meaning and pronunciation; the 'u' is an historical artifact of an obsolete romanization system. Even the glyphs 'フ' and 'ハ' are used -- among other things -- to signify that a word is maintaining its foreign nature and not made Japanese.