Once upon a time I saw the Adsense search from Google as a service however I now look forward to when I upgrade my site to provide my own search capacity to have have got 13 clicks today in the search for 38c return is below a service to the future
will be putting the site onto php and then utilising my own search via php will then add whatever ads to that page not sure whether it will be Adsense as well
Sitesearch used to be ok for me on one of my sites - then I integrated it into my site ... haven't had a single click since integrating it while I used to get above 10% CTR when I left it as the default google search opening on another page. The search values are always changing - sometimes it would be low (or smart priced) and other times it would be normal. The long term would average out - and it does depend on what people are searching for as well.
I have the search to help my visitors find what they need. If they want to click on an ad or not it does not matter to me
It very much depends on what people are searhing for. Generally, search cpc is significantly lower than ads.
The key benefit of the search facility is it shows webmasters what people are searching for - and if your site lacks what they want and it is related to what your site is about, then you know what content is required. That is one reason why I had initially put search on my site - to find out what people were looking for in my site so that I could provide better information to them and increase repeat visitors.