Wouldn't it make sense to offer

    git annex pull

which would basically do

    git pull
    git annex get

and

    git annex push

which would do

    git annex commit .
    git annex put # (the proposed "send to default annex" command)
    git commit -a -m "$HOST $(date +%F-%H-%M-%S)" # or similar
    git push

Resulting in commands that are totally analogous to git push & pull: Sync all data from/to a remote.

> Update:

This is useful:

    git config [--global] alias.annex-push '!git pull && git annex add . && git annex copy . --to $REMOTE --fast --quiet && git commit -a -m "$HOST $(date +%F--%H-%M-%S-%Z)" && git push'