Dealing with Stock Images without Transparent Backgrounds

Hello All!

I am ready to pull my hair out. I am looking for simple vector images in Stock, and every single one I license and download has a white background. I have tried opening them in illsutrator soI can just remove the white background, but when they open in illustrator, they do not have layers and are flat images. 

I find it silly that I can't just easily remove the background from the little vector right in illustrator, but as much as that annoys me, I also tried to bring it into photoshop to remove the background. The simple background remover in the properties window did not work well - despite the fact that it's a very clean vector with sharp lines, it still cut off half the image trying to remove the background. 

Any tips would be greatly appreciated! It's silly to think my old version of Microsoft Publisher removed backgrounds so quikly and easily (I know, *gasp*) and here I am with a state of the art design program that requires I take an hour to trace lines to remove the background of an image.........

Someone please tell me there is a better way than this??