But is there actually any significant desire for storm petrel eggs, to make the trouble of collecting them worthwhile?

I suppose there might be, but nobody's actually mentioned it. Is the ban on trafficking a reflexive reaction of the environmental law machinery, or is there some culture or culinary fad that puts a premium on the eggs?

Sigivald,
the ban is on imports of endangered species and products based on them (e.g. ivory from elephant tusks). I doubt if it is necessary to specifically prohibit the importation of storm petrel eggs. Of course some countries may have different legal mechanisms for dealing with this.

The EU (and its member states) are part of the CITES convention, which deals with trade in endangered species.

http://www.cites.org/

One imagines that CITES will get round to listing the New Zealand Storm Petrel on its next round up.

Quite how effective CITES is at protecting species is a matter for debate. With birds, it's true that merely being identified as rare could be a problem, because there are still--amazingly--fanatical egg collectors. But normally the practical problem with such protections is that they are hopelessly ineffective, because if there is a demand for the products it tends to be without regard for their cost (environmental or monetary). It's like the War on Drugs, save that narcotic plants can be cultivated. Not an easy problem.

It is certainly conceivable that market solutions would do a better job, but the problems they'd face are not too dissimilar. Making a schema for ownership of anything wild is difficult enough. And a lot of endangered species tend to be found in parts of the world where property rights of any kind are ill-respected. (We civilized capitalists generally wiped out most of the exciting neighbourhood species before our neighbourhoods got sound property and became capitalist.)