I've been busy and unable to reply. Polite sage to avoid necroing an otherwise dead thread.
The reason why it is a shit-for-brains idea to declare war on America is because that is what the American (((government))) wants. If you're stupid enough to declare war on America, then this allows the US government to claim, once again that it's fighting a defensive war and all the little lemmings will rally behind this great patriotic war.
That hasn't stopped them in any of a dozen other times from going to war. Afghanistan, Vietnam, Laos, North Korea, Iraq, none of them declared war on the USA. Neither did 1812 Britain (the US unilaterally declared war on them), nor did 1898 Spain, and none of them were even considered as threatening American vital interests, it was merely stated to be beneficial to America (1812 they could take Canada + expand west; 1898 they could dominate the Caribbean and Pacific). But the most relevant example is WWI, where the US declared war on Germany after the Germans started sinking war materiel that was shipping to England. This is almost the exact same situation as WWII, involving the exact same countries, and what do you know, the US declared war on Germany and fought until the close of the war. So if you think it matters that it was Germany declaring war on the US rather than the inverse, you have to explain why it didn't matter a mere 24 years prior with the exact same people, especially when the US government has neither before nor since particularly cared what the casus belli is nor who started the fight. It's useful for propaganda, but if that line doesn't apply, they'll find another one, just like they've done in every other war.
Furthermore, declaring war on a country that you can't even attack is so fucking stupid that even YOU know that it's dumb.
Like in 1776? There is such a thing as a defensive war.
More to the point, in a war of attrition, would you rather sink a million rifle rounds at sea, or face a division equipped with those rounds? Clearly it's better to destroy materiel in transit, but that requires sinking American ships. Even when it requires sinking British ships, the Americans may still consider it an act of war like the Lusitania. But, in order to sink ships, Hitler has to command his navy to start sinking vessels. If you say, "well why don't they just sink the ships without declaring war?", but that's simply not how the German mind works. You might get a few commando types to do it, but certainly not the whole German military.
The Germans highest ideal was the noble knight, like Lohengrim or Parcifal. Someone who fights to the death for honor and glory. The greatest naval hero of WWI was Karl von Mueller of the SMS Emden, which alone raided commerce in the Indian Ocean against a vastly superior enemy force but constantly put itself in danger to avoid civilian casualties. The man didn't even write memoirs about his exploits because he thought it would be too vainglorious.
The U-boat crews followed this logic, as demonstrated in the Laconia incident. U-boats by their nature are not ideal for rescue operations, but after sinking a troop transport the u-boats stopped to help survivors and told the Americans where to find them. The Americans send a bomber to attack them, and after the first one gets attacked and is forced to dive, a second one, assuming no one would be crazy enough to shoot at a rescue operation, proceeds to surface and again gets gunned at while rescuing sailors while under a red cross.
You may call this behavior crazy, but this is precisely the ruleset that Europeans were supposed to follow in war. More importantly, it was this heroic ideal that allowed the Germans to win constantly while outmanned, outgunned, and surrounded by enemies. The Americans and British, composed of Germanic stock themselves, couldn't even come close to matching the man for man fighting qualities, and even after the Russians copied their tactics they still had to outnumber them vastly to win.
You may consider it obvious that numerical advantage would win eventually, but in 1941 that theory had already been tested and found wanting. Perhaps the superior fighting spirit and innovation would overcome the material advantage of the allies? Obviously it was a gamble, but on the one hand, they might win, and on the other hand, what choice did they have?