Breadcrumbs help with navigation purposes and are there for the user experience. Personally, I feel as though they provide a greater user experience.
I would do some analysis work and put a heat map on your site. Try using hotjar they have a free subscription model that I think will come in handy. You can also see where users are clicking the most etc. Do you some research and analysis work before removing elements. Also, Google is not going to de-index pages just because you remove bread crumbs so you have no worries there.
Personally after looking at your attachment I would remove the entire far right column and widen all the other elements. You already have the "click here" button and everything else seems a bit redundant.