Nope, as far as I have known and tried, there is no sure hit software for background removal and that too in bulk. Yes, i know plenty of software and sites for background removal, but they are at most average because all of them requires manual intervention even though the process is automated. Meaning, AI removes not only the background but also a good portion of the foreground too that makes the image broken.
So, assume you have thousands of photos and you run through background remover, and keep the AI mistakes at the rate of 10%, what are the chances of you discovering the said 10%? You will have to waste your time manually looking at each image to get rid of the broken images.
If the rate of broken image is more than 10%, then there is no use in using automated bg remover and if the percent is lower than 10%, it will become that much harder to look for the broken one from the original one, unless and until the bg you are talking about removing is distinctive that all it takes to tell that image is broken or not is just one look.
Bottom line, invest your time and do it manually if the images are worth it.