1. The "same background" doesn't really exist for most cameras in most settings. Changes in illumination alone will make segmenting the background tricky. Moving objects in the scene will also be hard - think fountains and trees in the wind. Google for "foreground-background segmentation" to see some papers on this.
2. I haven't seen anyone use recent ML algorithms with less than high quality images. That may not matter, but it could matter a lot.
3. Extending recent ML algorithms to work with video at a high enough frame rate to be useful (10Hz at a minimum) may or may not be easy.
I'm sure that what you're proposing could be done. But I think that the number of small annoyances you'd hit would probably discourage most people who aren't treating the problem as a research exercise in Computer Vision.
If you would like to play with some of this stuff, take a look at OpenCV. http://opencv.org
Convolutional neural nets are the state of the art for this, specifically deep residual learning (http://arxiv.org/abs/1512.03385). It requires a good deal of background to understand what's going on and tune/implement the models, though, even if you just use the frameworks already out there. You probably don't even need that much data - you can probably grab pre-trained models and train them on a small additional dataset you collect.
They can definitely handle arbitrary backgrounds, although having a standard background makes the problem even easier, again.
Most deep learning computer vision algos are trained on 256x256 images, so having even larger images is just fine (you can downsample, or maybe even add up the predictions of different crops).