The more times you change hotels, the more time is wasted with checking in and out, getting oriented in the new city, etc.--not to mention the hours spent observing Europe through the windows of a moving vehicle. That means less time for sightseeing. Yes, you will set foot in more cities, but you won't see much in any of them.
Spain is large, and the car will be much slower than the AVE trains connecting Barcelona - Madrid - Cordoba - Seville. Use ViaMichelin.com for estimates of driving times along your route, keeping in mind that they don't include stops, getting lost, looking for parking, or getting from the parking place to your hotel or sightseeing target.
I trust you are planning to rent a car with a large enough trunk to hold all your luggage/backpacks out of sight. You need to have nothing visible in the car when you stop for sightseeing or a meal on hotel-change days.
Edited to add: Off the top of my heaf, these are places where you shouldn't plan to show up and buy a ticket; I'm sure I've missed some.
Barcelona: La Sagrada Familia, Parc Guell, Casa Mila, Casa Batllo, Picasso Museum; perhaps also the Palau de la Musica Catalana.
Madrid: perhaps the Palacio Real. There might sometimes be lines at the Prado.
Cordoba: Mezquita
Seville: Alcazar. See Rick's book for dealing with the long ticket line at the cathedral.
Granada: Alhambra (sells out months in advance)