AnkiMobile developer here. Are you referring to the mobile app or the desktop app? Because the desktop has API endpoints you can hook into with extensions [0]. If you're talking about the mobile app, I believe we originally decided not to provide an extension API because Apple forbids it.
I am talking about a REST API that hooks into your AnkiWeb infrastructure. I believe I asked about this in one of the google groups and was told you aren't interested in doing that because of the additional load it could put on the service. I would love to put together something like the Evernote webclipper for creating cards right here in the browser without doing this awkward alt+tab+click+click+click+etc dance to create cards on the desktop client. I admire the work you and others have done on Anki and its extensions, but if I'm going to use Anki as my primary learning tool it needs to be delightful and effortless to create/delete cards as needed.
Ah OK, in that case I can see both sides. From Damien's perspective, AnkiWeb is a free service, so development/support time and server load have to be considered for any new feature. From the user perspective, web clipping tools would be really nice.
Is there anything to prevent interacting between the desktop app API and a web clipping browser plugin, in the same way that the Zotero connector plugin does with the Zotero app API for example?
[0]: http://ankisrs.net/docs/addons.html