Sorry you feel this way.
Galveston is an island with approximately 52,000 residents. Transportation is private enterprise; not affordable or viable for a city to take on. There is no passenger train and hasn't been for decades. Even Amtrak has few passengers going east or west and is unreliable. The tracks are controlled by the railroads, not the City. Bus service stopped over a decade ago due to no riders.
Same with car rental, it is not economically feasible and a logistic nightmare. Hertz made the decision to leave in 2008 due to economics.
Galveston is a destination, entertaining over 7 million visitors annually, As with the majority of resort towns, minimum stays are required. Many have a 3 night minimum. as we recently discovered. It's not price gouging, it is business.
Businesses know to perform due diligence to see if economically feasible and profitable. The island being just of the mainland, does not meet the economic requirements for numerous entities. The City has nothing to do with what you are asking. Just as cruise lines provide transportation ONLY on sailing days, not 7 days a week - economics!