It was war anyway.
ISIS had basically already declared war on us. They don't say leave us alone and we'll leave you alone. They will come anyway because they hate us because we are not with them.
As far as they are concerned there are two positions: with them and all they stand for, anyone else is against them. There is no neutral.
If we hadn't gone in it could well be a case of:
"First they came for the Socialists, and I did not speak out—
Because I was not a Socialist.
Then they came for the Trade Unionists, and I did not speak out—
Because I was not a Trade Unionist.
Then they came for the Jews, and I did not speak out—
Because I was not a Jew.
Then they came for me—and there was no one left to speak for me."
I am also certain that if there was a viable way of sending the Secret Service in and sorting it then they would have done that. If nothing else it would be much cheaper for them.