They would have bided their time and waited for the next election. Because there is probably still going to be a next election in Egypt, despite the coup, and now the Muslim Brotherhood might actually win it.
There is a good deal of chatter in the media at the moment about the ''end of the Arab Spring'', some of it by commentators who can barely conceal their delight.
Egypt, with almost one-third of the world's total Arab population, was the great symbol of the democratic movement's success, and now Egyptian democracy is in a mess. But the drama still has a long way to run.
Mr Morsi is now under arrest, as are many other leading members of the Muslim Brotherhood, and the passionate demonstrations and counterdemonstrations in the streets of Egypt's cities make it hard to imagine that any compromise is possible.
Indeed, Russia's President Vladimir Putin warned last weekend that Egypt risks stumbling into a civil war like the one that has devastated Syria.
Opposition leader Mohamed ElBaradei, on the other hand, justified the military coup by claiming that it had been the only alternative to civil war - which could, he said, have been as bad as Somalia.
Really?
One suspects he doesn't know much about Somalia. Indeed, one suspects he doesn't really know much about Egypt either (he has spent most of his career abroad).
There was no risk of civil war in Egypt before last week's military intervention, and there is no risk of civil war now either.
What we are seeing is a fierce struggle for power between rival political movements, in a system where the political rules are newly written, hotly disputed and poorly understood. And all the players have made some serious mistakes.
The Muslim Brotherhood, on the basis of last year's 51.7% majority for Mr Morsi in the presidential election, assumed that it had the unquestioning support of half the population. This was probably not true.
Many voted for Mr Morsi in recognition of the Muslim Brotherhood's long resistance to six decades of military dictatorship. Others voted for him in gratitude for the Brotherhood's unfailing support for the poor, or in disgust at the fact that Mr Morsi's only opponent in the second round of the election was a leftover from the Mubarak regime.
Perhaps as few as half of them actually voted for the Brotherhood's core project of Islamising Egyptian law and forcing its own version of Islamic values on Egyptian society - but the Brotherhood seemed to think they all had. Even if that had been true, trying to impose fundamental changes on a country with the support of only half the population was not wise.
Some of the constitutional changes Mr Morsi imposed, and some of his tactics for pushing them through, may actually have been the result of political compromises within the Brotherhood, where he constantly had to fend off the fanatics who wanted even more extreme measures.
Nevertheless, the secular opposition parties inevitably saw him as an extremist, and genuinely feared that he would somehow manage to force the whole package on Egypt.
So the secular parties responded with extra-constitutional tactics of their own: mass demonstrations that were explicitly intended to trigger a military takeover that would sideline Mr Morsi and the Brotherhood.
In only four days of demonstrations, they succeeded, in large part because the army, a resolutely secular organisation, had its own grave misgivings about where Mr Morsi's government was taking Egypt.
But the army hasn't actually seized power. It has appointed Adly Mansour, the head of the Constitutional Supreme Court, as interim president, with the task of organising new parliamentary and presidential elections.
It will not be possible to exclude the Muslim Brotherhood from those elections without turning the whole process into a farce - especially since the Brotherhood will probably be going through some changes of its own.
The Muslim Brotherhood took little part in the 2011 revolution, and the men at the top, including Mr Morsi, were utterly unprepared for power.
They are now likely to be replaced by a younger generation of leaders who are more flexible and more attuned to the realities of power.
They might even win the next election, despite all Mr Morsi's mistakes this time round.
That's the real irony here. If the opposition parties had only left Mr Morsi in power, his unilateral actions and his inability to halt Egypt's drastic economic decline would have guaranteed an opposition victory at the next election. Now it's all up in the air again.
But democratic politics is far from over in Egypt. Foolish things have been done, but the Arab Spring is not dead.
• Gwynne Dyer is an independent London journalist.
