So the context for this characterization of events is quite real, but the Mitscher's motivation for this particular decision was probably not to prevent a battleship clash for political reasons.

There was a rivalry in the U.S. Navy between aviation officers who had begun their career as pilots and more conventional officers who had only learned to fly later in their careers or never earned wings. This rivalry was often called the Brownshoes (aviation) versus Blackshoes (battleships). Obviously, in the long view, the Brownshoes were correct about the future of aviation. However, the Blackshoes were not (by 1943 onwards) seriously trying to preserve the dominance of battleships, everyone knew that ship had sailed, so to speak. The Blackshoe position was simply that seniority and leadership ability, and ability to handle ships should be taken into consideration as much as tactical proficiency in handling air operations. The Brownshoe position was a basically that Blackshoes were proven to be inadequate in command of carriers and should be relegated to subordinate positions despite their seniority. The Brownshoes were very loud about these views and the debate occasionally spilled out into period news articles and historical accounts. Every time a Blackshoe made a less than perfect decision, there was a Brownshoe on someone's staff explaining how this was what happens when you put battleship guys in charge of carriers.

However, the Spruance-Mitscher relationship was a fairly businesslike one and generally not a manifestation of the Blackshoe-Brownshoe rivalry. Mitscher and Spruance had been a command team for about 18 months and they had become used to working together. Spruance's command style generally was to avoid micromanaging his subordinates, and he gave Mitscher considerable latitude in managing the Fast Carrier Task Force, which contained most of the air striking power of Spruance's 5th fleet. It is not particularly out of the ordinary that Mitscher formed an airstrike without consultation with Spruance, that was more or less their normal method of reacting to sighting reports and unplanned events.

The other relevant bit of backstory here is the Battle of Leyte Gulf six months earlier. During this battle, the other Pacific Command Group, Adm. Halsey's 3rd fleet (which was more or less the same ships under a different command team) had faced a similar situation of covering an amphibious operation against Japanese counter attack. Halsey had assumed during this battle that air strikes had crippled a Japanese battleship force after they had sunk the Yamato's sister ship the Musashi and scored bomb hits on Yamato. He neglected to leave a battleship covering force for the invasion fleet and allowed Japanese battleships to get close enough to the invasion fleet and it's escort carriers to inflict some damage and cause a near disaster. Yamato's guns had not only chewed up the escort carriers, they had damaged Admiral Halsey's reputation.

During the Okinawa campaign, responses of Admirals Spruance and Mitscher reflected the combat experience of Leyte. The Japanese surface sortie was therefore taken completely seriously despite it's forlorn hopes. Spruance made sure the invasion was covered by Surface forces. Mitscher made sure that U.S. airstrikes were thorough in beating back the IJN heavy ships. There is no percentage in letting the Yamato and it's escorts get close enough to fight a gun duel, and the blackest of Blackshoes was aware of this. Spruance was merely taking an extra precaution, and Mitscher was doing his job in making sure it was just a precaution.

Anyways, a brief historiographic note. It seems the wikipedia source here is Morison, who wrote the official U.S. Navy history immediately after the war and was present in person for the Okinawa campaign. He presence meant that he was able to take firsthand interviews about the Blackshoe-Brownshoe rivalry when it was still hot (edited for clarity). My answer is based on Ian Toll's recent three volume work, which has a bit more distance from events and in my view a more nuanced understanding of Spruance and Mitscher's command relationship.

Slightly off topic but during the Battle of the Philippine Sea there was also the potential for a major surface action on the night of June 18-19. Much has been made of Raymond Spruance's decision not to push West with his carriers but if he had been extremely aggressive he could have also pushed his heavy surface units forward to attempt to fight a nighttime surface action with Ozawa's forces.

On paper this sort of a battle should have heavily favored the USN. They had more modern battleships and far more advanced radar. Willis Lee, who was arguably the most prominent battleship admiral in the USN at the time was strongly opposed to such a move. He knew that a nighttime surface fight was inherently chaotic and risked giving the Japanese an upset win, or at least the opportunity to inflict disproportionate losses. He was also concerned about how well his crews were trained for a night surface battle.

Most of my information on this comes from James Hornfischer's The Fleet at Flood Tide which covers the Marianas campaign in considerable detail. I have not been able to find a source that analyzes the potential for a surface fight in great detail and I remain unsure if the IJN and USN forces were actually close enough to have reached each other that night.