I've booked several "DIY" holidays as you call them. Mainly to Florida.
There is a good reason for this. To book a package with a company means that you pay for flights, accommodation (we always book a villa rather than stay at a hotel) and car hire. However we have issues with this system and in particular the accommodation.
Many travel companies only offer Villa's on allocation when you arrive at the airport. This means that you have no idea where you will be until you speak to a rep and receive the code or key to the villa you are staying at. I've heard and read horror stories of families turning up to Villa's that are in a terrible state of repair or are miles away from the main attractions. There was no way we were going to risk that happening on what was an expensive family holiday. Also we felt the prices being asked were a little high compared to what we could find privately.
Therefore we booked flights, car hire and accommodation separately. In doing so we got the best price possible for the car hire and flights and found a villa that not only was exactly what we wanted, where we wanted and had excellent facilities, but was also cheaper than what a comparable villa would have cost us as part of a package deal.
However what put us off the whole package deal with the travel companies, was not the cost, or the fact we felt it would be cheaper doing it ourselves. It was the lack of knowledge about where our Villa would be, it's state of repair and the distance it would be from the main attractions. To travel not knowing where we would be staying felt too uncomfortable.