I've had the opposite experience to most on here - I've ended up essentially with free hotel when booking a package with British Airways holidays on more than one occasion.
I usually check out all th options when booking holidays, and usually prefer booking separately when our family of 3 travel together and want two rooms, but I have found that quite often, for a solo or couple, a package with BA is cheaper.
An example being a holiday I have booked for next year. I wanted to go to a specific hotel in Antigua. I checked out all the hotel booking sites (and the hotel's own website)and the flights with both BA and Virgin from the UK, and I ended up with what I consider a bargain.... I got an all inclusive package flying Premium Economy for just a couple of hundred pounds more than most sites were quoting me for the hotel alone! A similar sort of thing happened with a break to Thessaloniki in Greece.
I agree, it doesn't always work, but when it does it saves a fair bit!