For me, unless you are touring very sparse areas like small towns and villages of Asturias or Galicia, a car is absolutely a drawback over a benefit. Weekend trips from any decent sized city in Spain are exceptionally easy via train or bus. Parking in any large city is no fun at all and traffic coming in and out of large cities, as well as within larger cities, can be a nightmare at certain times. All three cities you mentioned (Valencia, Malaga & Alicante) are very well connected by train and bus and it's super easy to book tickets same day using the Renfe app, Alsa app, etc... and head out on a day trip/weekend trip. I spend a few months a year in Spain and have rented a car one time, for 2 days, and that was to explore the more rural areas of Asturias. Other than that, I've never even considered it.
Thank you for sharing your experience :)
There is also BlaBla car for between cities.