The "purge the galaxy" bit was implied later in Voyager to be just a shock-tactic: make yourself sound much more ruthless than you actually are to scare away potential opponents.
At least that's how I rationalise the post-Scorpion retconning of the Undine.
Scorpion Part I
After escaping the first bioship. Kes says what she heard the pilot say:
Kes:...the weak will perish.
When Voyager finds the singularity Species 8479 are using to enter this Universe:
Kes: Yes, I can hear them. They come from a place where they are all alone. Nothing else lives there.....I feel malevolence, a cold hatred, the weak will perish. It's an invasion. They intend on destroying everything.
So it was established in Scorpion Part I that Species 8472 was out to destroy everything, not just the Borg.
So the Borg would have been the lesser of 2 evils. The Borg had already destroyed hope of diplomacy by invading their space. Picard would have had no choice.