The thing is Itami isn't that stupid. The Empire already knows how strong the SDF is, they've lost 5-6 armies to it.
But what they didn't know is how little the cost is for the SDFs overwhelming power. It doesn't take them years of weaning dragons for aerial cavalry, it doesn't require mages upon mages. What Itami accomplished with the "basically nothing" peace accord is showed the Princess that the overwhelming display of power they saw firsthand is something the SDF can routinely do. One of their soldiers can kill a dozen of their shielded fighters in a matter of moments, their armored Pegasus can take out half a battalion is less than a minute...and they brush it off as no big deal or cost.
They took a pittance for all that effort. A tax exemption, a request that the enemy combatants are imprisoned and not executed, a little information, and a handful of exotic prisoners. They expected him to ask for the entire city or huge shipments of grain.
That peace accord was more horrifying to the Princess and her attendant than the display of power.