Now consider the times the country has gone to war without a formal declaration: Korea, Vietnam, and the two Gulf wars.
Do you see a difference in results between the first set and the second set?
Add the Barbary Pirates, who like the Taliban were not a nation-state (at best, a rogue state). There was no formal declaration of war there, so was it unconstitutional?
Getting to Iraq, GWB did not even need authorization of the use of force by Congress. Iraq violated an active cease-fire agreement and the military action originally approved in 1991 could easily recommence without additional authorization. Congress voted on the authorization as a political act, not a constitutional one, to show that they still supported the effort. (And, being a political act, to also put anti-war opponents on the record.)