The medevac argument won't work in Sydney because the major hospitals all have their own pads.
We did have a CBD pad in the 80s, in Darling Harbour, and it was popular. When the Gummint developed the DH area, the pad was moved around the corner, but the paperwork wasn't done properly, and the NIMBYs shut it down.
We almost got it back in 92 but an election was called, as Belly Tank described, and the cowardly parties bowed to a certain noisy female in Balmain.
Ironically, that noisy female eventually became the minister for tourism, and wouldn't a CBD pad help tourism!
The floaties are there on a Grandfather clause, because Rose Bay was always a flying boat base - my father used to fly the old Empires out of there. One option was to put a floating helipad into the designated water aerodrome, but the environmental requirements knocked that on the head too.
With the Olympic planning back in 1998/99 we thought we might get a CBD pad, but missed out again. Bluddy NIMBYs and spineless politicians.