Actually, this is behind one of the great debates in this part of the
world. The "plant xenophobes" would rid the continent of *all*
exotic plants if it were possible. But as a start they've picked on
coconuts (along with very few other species -- and not including
wheat, maize, potatoes, sugar cane, apples ... but you get the
point .

Seems there's a view that coconuts are not native to Australia. Given
that they are dispersed so readily by sea as you point out, and they
occur all around large parts of the Pacific, it's really hard to
believe that they didn't arrive "naturally" in Australia too.

The "death to coconuts" gang suggest that the Great Barrier Reef may
have prevented them coming ashore where they would have been best
adapted. (And they may have a point when one looks at prevailing
ocean currents -- but one of my mates also suggests the aborigines
just ate them as fast as they arrived! ;-)
Cheers, Phred.

+ + +
Introductions are a matter of great debate here either, but nowhere near the
problem they are in Australia. The flora and fauna in Europe are pretty
tough so that most invaders have a hard time of it.

Nevertheless from time tot time gardening centers have to be forbidden from
selling yet another cute pond plant or animal when this goes out of control,
being dumped in the wild by garden owners and then running amok.

At one point there was also debate on having the forests here producing more
wood so as to limit wood imports, but the only trees to produce (relatively)
high quality woods are 'exotics' such as Pseudotsuga and Robinia. Nowadays
all the useful trees are weeded out of the forests as 'exotics' and forest
owners are going out of business.

On the other hand rabbits (introduced by the Romans) are now somewhat
protected, mostly since hunters like to shoot at them.

Of course farmers don't grow any plant even remotely native.
PvR