The point of the UN Declaration is it makes governments, presidents and armies (and other bodies, perhaps even business corporations) accountable, outside of their own country too. Not in a regular court all the time, but before public opinion and in the realm of which other countries elect to cooperate with a flawed government, a state engaged in war crimes and so on. It's a sharp stab at the idea "Right or wrong, don't mess - it's my country!" This transnational scope is a vital thing about the Declaration, and that's why it mattered so much to the wave of colonial liberation in the 50s and 60s, and to the radical opinion back then.
I'm the first to admit that most of the regimes in those countries don't live up to the Declaration at all, and that there's a lot of hypocrisy going on, but that shows democracy takes time to get established and strike roots. One can't compare with the USA: the thirteen didn't begin in state of wasted, scorched country and once they had driven out the English (with vital help from the French!) they were not ringed with hungry enemies armed to the teeth - then the revolutionary wars in Europe meant no one had time to bother with America for a while. Countries such as Pakistan, Eritrea, Zimbabwe or South Africa have never been in that fortunate situation.
"You can't take a country to court now over its violations of basic human rights, so the UN Declaration is worthless". Well, in many countries the Head of State can't be prosecuted or even questioned by police either, and even when he is not immune, it's often de facto impossible or unthinkable to make charges against a prime minister or a commander-in-chief. Richard Nixon was pardoned by Gerald Ford, so he couldn't be taken to court over Watergate; President Chirac of France (1995-2007) has had pending trials and big scandals hanging over him, but he was in legal immunity while president and the major things will likely never be cleaned out in court now. Politics sometimes overrides justice, but that's not unique to the UN.