Shocking as it may be for you to accept, with your inflated, American exceptionalist, opinion of the global power and importance of the United States, but the governments here in the EU do not ‘cave in to US demands’ or even particularly give a shit about them, (ditto for the general populace) but are generally more worried about public opinion and how it will effect their chances of re-election and there is a history of EU opposition to US policies, corporate pressures, and geo-poltical stances, to demonstrate this. A relatively recent example being the refusal to aid the US in its desire to bomb Syria.
In relation to the Assange case, this business was implemented by the previous Swedish right wing government and still is by various individuals who have strong personal connections with Karl Rove and the American government and is nothing to do with the present Swedish left wing government, who, if anything, have put pressure on the prosecuters to resolve the matter quickly. Generally it is out of their hands. Or are you suggesting that government should interfere in legal process, which is the hallmark of tyrannies?