Almost. For energy and broadband, where you actually have a choice — Bill compares deals from all the main suppliers. Not literally every supplier in the market, but all the ones you'd want quotes from.
Water and council tax work differently: your water company is fixed by where you live, and council tax is handled by your local authority, so there's no switching to be done. Instead Bill registers you with the right water company and lets the council know you've moved. Same idea with your TV Licence: only one place to get it, and Bill sets this up for you.