Now I tend to perfer the TOS federation as it was less arrogant and naive, but to answer your question becuase their "contingency" was to commit genocide.
Not only that but it wasn't anywhere close to a justified response seeing as at that point the Dominion was just like every other empire the Federation clashed with heck the "people who overtly stated their intent to take over the rest of the galaxy and impose their system of beliefs on people" pretty much describes the Romulans, Klingons, and Cardassians and all three of them sent disguised spies into the federation to disrupt it and the federation never decided to commit genocide against them.
I think it's fairly justified after the Founders wiped out New Bajor, declared that they would impose their order on the galaxy, caused the destruction/crippling of the Obsidian Order and Tal Shiar, created a slave race that was addicted to drugs, and attempted to cause a war between the Federation and Tkzenthi. Aside from a few examples like Odo and Laas (who were deliberately flung out into space), the entire species
apparently supported xenophobic and expansionist policies and refused to negotiate a peaceful resolution to the conflict. In a case like that, genocide is the only practical contingency.