The times I’ve shipped cars, I had the shipping accounted for in the purchase/lease. This way the onus is on the dealer and if anything goes wrong and they co-ordinate everything, saving me the hassle. Plus a dealership can almost always get better rates than you will.
Some dealers don’t want to take on that liability, some do.
Fly in and drive can save money, but how much is your time worth? If I have to spend 4 hours getting there and 10 hours driving back, is that worth saving $1000 in shipping? For me, no. For others, maybe. Everyone’s time/value calculation is unique.
Plus after accounting for the miles you burn driving back, gas, cost of flight, cost to get to/from airport, a lot of times, the difference between shipping and fly/drive is a pretty small number. It’s so much easier for the car to just show up at your front door.