The golden arches over Baghdad

Vivid though it was, and irresistible to the world's media, the image was symbolically incomplete: when Saddam Hussein was toppled from his pedestal in Baghdad on Wednesday, no one had much idea who or what to put in his place. Ahmad Chalabi, the Iraqi exile favoured by the Pentagon, does not have sufficient stature, while Abdul Majid al-Khoei, the London-based Shia cleric, was hacked to pieces by a mob soon after he reached Najaf. Logically, what the statue-breakers and their American assistants should have erected in al-Fardus Square was Ronald McDonald's golden arches – perfect symbol of US global dominance, but also a warning about the danger of over-reach inherent in that project.

The war in Iraq has demonstrated not that we are all Americans now – an outcome millions of people would welcome, if it meant a share in American liberty and affluence – but that we are all subject to American will. And, ominously, that country's leaders have shown themselves much better at exercising their power than recognising their responsibilities. As the remnants of civil society in Iraq crumble in an orgy of ransacking – hospitals and the headquarters of aid agencies as well as palaces belonging to the old regime's elite – they do not seem to have given much thought to the practical consequences of their invasion.

Looters displaying the brand names of Western capitalism on the one hand, and children mutilated by US missiles on the other, have combined to create another eidetic image, of failed and almost randomly punitive modernity. Tell the little boy with no arms, Ali Ismaeel Abbas, that his body has been wrecked because of the US's passionate belief in liberty, and it would be a cruel mockery. Tell him that his family got in the way of the hard-faced neo-conservatives in Washington who now control the world, and you would be closer to the truth.

This is not a clash of civilisations, a phrase that means little in an age when CNN and the BBC compete with al-Jazeera, and when Muslim women spend hours in Kuwaiti shopping malls, trying on the latest hijab printed with the Chanel logo. Millions of Arabs hate the US, but they also want many of the things the country stands for, from democracy and freedom of speech – unthinkable luxuries in Arab states – to an endless supply of consumer goods. Even the band of mainly Saudi hi-jackers who supposedly started all this on 11 September 2001 displayed complex and contradictory attitudes to the West, attending its universities, absorbing its technology and socialising in its bars and restaurants.

The source of their rage was not Islam, although an extreme form of the religion appears to have supplied a twisted justification, but their hatred of America's role in the Middle East, where it has for decades shored up regimes every bit as intolerant of opposition as the one toppled last week in Iraq. Ironically, what the terrorists have brought about – more accurately, what they have provided an excuse for – is even greater American engagement in the region, the first in a series of externally imposed regime changes. The purpose is not to remake the world in America's image, a project that would require politically unacceptable levels of expenditure, but to make the world safe for the US. It is not about helping foreigners enjoy the American way of life – think of the cost of providing clean water for six billion people, let alone all the labour-saving devices Americans rely upon – but removing threats to it, regionally and globally.

It is an admission that selling America to the rest of the world, assuming that we would come to love the country through consuming its technology, movies, music and food, has not worked. On the contrary, it has created familiarity without respect, global recognition without affection, an unstable combination of desire, envy and loathing. Now the American government has responded not by doing things that will improve its image – sharing its prosperity with poor countries, and withdrawing support for dictators all over the world, not just in Iraq – but with a brazen demonstration of military might. We may not like what it is doing, but we certainly know who – for the moment at least – is calling the shots.