In my experience it is often that I search for something under the cursor, so it
makes sense for occur to pick up the word at point and offer that for search.

Also, if a region is selected occur could offer this as input.

I did these for myself long ago and it's a pretty useful hack which could improve
built in occur too.

So something like this for initial input :

(if (use-region-p)
(buffer-substring (region-beginning) (region-end))
(thing-at-point 'symbol))))))