Every major conflict has demonstrated that no nation has ever had the "right" mix of military capabilities' when defending themselves from offensive action. if they had the right capabilities they would have deterred the aggressor. I strongly believe there was no Soviet offensive in Europe during the cold war because of the huge US led NATO forces along the border.
Wars are defined by intent and capability on the part of the aggressor. Personally I don't see any evidence of either from Russia with respect to major hostilities against Western European countries. What I do see is an incremental strategy of undermining and co-opting the governments of border countries with diplomatic, economic, and military threats. There does not appear to be a coherent EU strategy to counter this move and absent that trying to develop a European army is IMHO, futile.
However I think the bottom line with respect to US intentions is becoming clearer. 40 years ago the idea that the full might of the US military industrial complex would be deployed to defend Europe from any aggression was unquestioned on both sides of the Atlantic. Today I would suggest that the US appetite for defending Europe is much reduced and is very situationally dependent.
Finally unity of command is the bedrock principal of effective militaries. For example one person, the US president, is the "Commander in Chief" of all US military forces, so even if a "European Army" is created how will it be effectively deployed by an institution which requires the unanimous approval of all member states for every major decision ?