[mironicus]

You just pointed it out. In most cases the use of the flyswatter is just for comedy and to stop some perverted attacks. It's a supporting tool for her. She also used the flyswatter to stop Kodaka and Sena from kissing during the King Game. Mostly she tries to control/suppress others with her insults (Sena), manipulations (Kodaka, Sena, Maria, Yukimura) and physical attacks (Maria, Kodaka, Sena).

[mod edit: removed spoilers for unanimated content]

You can't really ignore the fact that there is fear in the air if Yozora switches to her evil mode (sometimes it's fun, sometimes it's disturbing). And for example while Kodaka was able to protect Sena from three guys because he was just used to protect himself from delinquents the whole time - handling Yozora is much more difficult. You never know what she does next.