Until she succeeded Celestia, That was outside of her remit and for some reason Celestia believed the EEA had authority over her school (and hence her!) so Twi was clearly not even in the running.
I am assuming it was a case that, as headmare of a school, Celestia was subject to the EEA's authority but as Princess Celestia, she wasn't - but Princess Celestia didn't want to abuse her authority to get special treatment while wearing her other crown as a headmare.