We have driven many, many times and overall, I think the greater sense of control is an illusion.
Transport time via bus or car is essentially the same. What that leaves you with is wait time at the bus stop vs the amount of time it takes you to drive through the vehicle entry, park and make your way to the park entrance. Assuming Disney bus wait times are within the 15-20 minute standard, I doubt you'd get there any faster driving. And you're adding another 1/4 to 1/3 mile of walking to the beginning and end of your day.
Driving is a hedge against the outliers--those times when waits are longer than 20 minutes. How often that happens is open to interpretation. We recently stayed at SSR for a few days and exclusively used buses. The only time we waited more than 20 minutes was (ironically) coming back from Magic Kingdom where it doesn't make sense to drive. We had one other wait of about 20 minutes and others surprisingly were only 5-10 minutes maximum.
As others have said, driving also gives you flexibility that buses don't. You can drive straight from a theme park to Disney Springs or resort-to-resort, trips that are difficult with Disney transportation.
I priced rental cars during our visit and the lowest rates were $60-80 per day. At that price, I'd personally go with an Uber for urgent needs and pocket the savings.