Given the dictatorial nature of most governments that exist today (and the tribal rule and/or anarchy that exists in huge, ungoverned areas of the world), it is inevitable that a single, one-world government would be authoritarian and/or that most of the world would live in a state of anarchy.  In either case, the prevailing principle would be, "might makes right" and there would be little or no protection of individual rights and liberties.  

Historically, nearly all people on Earth were been ruled by monarchs (who initially arise via military conquest and the resulting enslavement of weaker tribes), until the recent rise of republics (which protect the individual from tyrants) that occurred only within the last few centuries.  Before 1776, there was only one free republic in the world:  San Marino.  After the Treaty of Paris in 1783, there were two.  Since then, constitutional republics -- with limited powers of government, under the notion that "governments are instituted, deriving their just powers from the consent of the governed," … “in order to protect [individual] rights” -- have arisen in much of the world, but it remains a fact that the overwhelming majority of the seven billion inhabitants of this world are still ruled by dictators (i.e. one-party states and/or monarchs with essentially absolute power, wherein citizens have only those rights that the ruler chooses to grant them!)

John Lennon's notion is both nice and naive.  If there is no enforceable limit placed upon the POWER of the government, and if that power is subject ONLY to democratic vote, then the majority will always vote to control the minority and, eventually (as successive minorities succumb to the will of the majority), nearly everyone will be under the rule of by the most-successful politicians -- who will own the military, control the economy, and limit individual rights as THEY see fit.  Without enforceable limits to government power, and with only the protection of democracy (wherein two wolves and a sheep can vote on what to have for dinner), there is no hope for the freedom of the individual and civil liberty.  

Imagine that the 200 or so nations of the UN voted on what sort of world government to create.  Assuming that each would favor something like the governments they already have, isn’t it clear that the result would be one-world dictatorship that resembles perhaps a cross between China under Mao and Iran under the Ayatollahs, or maybe a blend of  South American gangster-governance, Saudi authoritarianism, Putin’s post-Soviet Kremlin rule, and recent sub-Saharan anarchy.  Regardless of which form of one-world government won the UN vote (or the world-wide plebiscite), the result would be a plunge back into the tyranny from which a minority of humans emerged only within the past two centuries.  Nice as the nostrum may sound, a one-world state today (and in the foreseeable future) would spell a permanent end to the fragile but embryonic development of new nations wherein peaceful citizens can live freely, under a government they trust to protect their individual rights from attack by others, rather than living in constant fear that their liberty can be arbitrarily curtailed by the unlimited powers of that very same government.