Popular search terms are used on many popular classified website.(Maybe you have not seen them before)
You can always remove those urls which do not have result.
Real time indexing, Really! Are you serious!
That by using breadcrumb(be it yours or any other) can make your site indexed in real-time?
Do you run any big website or worked as admin of their webmaster dashboard?
It seems you misunderstood the concept about Google webpage indexing.
No way you can make your site indexed in Real-time, It will be indexed very quickly(Not real time) if you have big website with frequently updated content.
With sitemap you make indexing easier for google-bot, that's it.
Indexing speed is also dependent upon how much faster your server respond to crawler.
It will not visit frequently if it increase your server-load.
Many factors related to indexing.
By creating sitemap you just making it easier to google-bot.
Of-course their is little work you need to do to manage your sitemap but rewards can be greater than that.
I sorry, but I am not trying to offend you. This is what I understand/worked/read in last 8-9 Years. I did not wanted to make it mine is good and your's is bad discussion.
I met many people who still think that proper meta-keywork-tags(keyword stuffed title/description) can rank their website higher and that is real BS. And people are still trying to sell it.
Anyway no offence this is what I know/read in my personal capacity.