The main advantage of a private car over a coach tour or the train is timing control — you decide when to leave, how long to spend at each stop, and when to head back, rather than working around a fixed departure and return time shared with a busload of other people. That matters most for destinations with a lot to see in one day, such as combining Stonehenge with Bath, or Oxford with a Cotswolds village, where a coach itinerary often allows less time at each stop than most visitors would like.
Popular destinations do get busier at certain times: Windsor and the Harry Potter Studio Tour are especially popular with families in school holidays, Stratford-upon-Avon and Warwick Castle see more visitors in summer, and Bicester Village gets busiest at weekends and around seasonal sales. None of that changes how the transfer works, but it is worth allowing a little more time at the destination itself if you are visiting during a known peak period.
For families combining a theme park with an overnight stay, or a day trip that starts or ends at an airport, mentioning the full plan at booking means the whole day is planned as one itinerary rather than several separate journeys.